{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52120,"title":"Compute the fractional derivative","description":"Cody Problem 1370 asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the th derivative as . Then a familiar example from calculus would be . \r\nFractional calculus involves derivatives in which the order  is not an integer. With  and , then \r\n\r\nWrite a function that computes the fractional derivative of order  of an expression of the form\r\n\r\nThe first input to the function will be a 2x matrix in which the first row is the coefficients  and the second row is the exponents . The output should be in a similar form. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 128.275px; transform-origin: 407px 128.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1370\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 1370\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.442px 7.79167px; transform-origin: 294.442px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.0083px 7.79167px; transform-origin: 49.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth derivative as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^q x^a\" style=\"width: 32px; height: 19px;\" width=\"32\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then a familiar example from calculus would be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^2 x^3 = 6 x\" style=\"width: 65.5px; height: 19px;\" width=\"65.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 179.725px 7.79167px; transform-origin: 179.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFractional calculus involves derivatives in which the order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.1667px 7.79167px; transform-origin: 71.1667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not an integer. With \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"q = 1/2\" style=\"width: 51.5px; height: 18.5px;\" width=\"51.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.79167px; transform-origin: 19.4417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.4583px; text-align: left; transform-origin: 384px 18.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^{1/2} x^2 = 8 x^{3/2} / (3 sqrt(pi))\" style=\"width: 117px; height: 37px;\" width=\"117\" height=\"37\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 196.292px 7.79167px; transform-origin: 196.292px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the fractional derivative of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 7.79167px; transform-origin: 88.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of an expression of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(x) = c­1 x^a1 + c2 x^a2 + c3 x^a3 +...\" style=\"width: 204px; height: 26px;\" width=\"204\" height=\"26\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.6333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.8167px; text-align: left; transform-origin: 384px 21.8167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.85px 7.79167px; transform-origin: 124.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first input to the function will be a 2x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.775px 7.79167px; transform-origin: 143.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix in which the first row is the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAoCAYAAAALz1FrAAAA9ElEQVRIie2VbQ2EMAyGHw9zMAMYOAUoOAc4wAEW0IAEPGABDWdh92NtRgjf2y65ZE/CDxi06du3BQqFQqEQjQVqoJXLpgz+AkZgBt5yPwAOaFIk6CTYsHquSWbAxCToJdC4cTbL2RSToJEgH7a1t3jZHldhJLjDy5UFrcIB1c1vDd559dmLI0Gqu3K8CYY4RKt40lSt5FSBmCSXmTieAYO3d5TrWkI16wZW+J6tJ90S5sqdJVCWze8kcY+vbk/vmu3tcEhFWIZXmqkrKMk+20N7mXQ7L7H8wJE6hNnWEARn6b8mi2TqxoGMjVcn3l2ohcI/8AWjzEUn2YFV5AAAAABJRU5ErkJggg==\" alt=\"ci\" style=\"width: 12.5px; height: 20px;\" width=\"12.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 7.79167px; transform-origin: 83.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the second row is the exponents \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAoCAYAAAAPOoFWAAABF0lEQVRYhe2UUQ3DIBCGPw84mAEMoGAK5qAO6mAW0FAJeJiFaqiF7aF3KWNlkJQt2cKX8FD+9n7uehx0Op1O52ewwACMgJM9J8+2pUkAZjFzgAduwF3WqYXRRYLNgEm0e6R91Cg2ux41OkfB3I5+KujVGGCRQFPmHc16YT/raka2U+e6LIgeMrqlsks1q1wgFx1mzLzjRffvjGoCBcqZa2ZvSxyX8LyjD2yZN/1fqdmF9RpMPJfZ81oFS0WX2sgssJ7cSDC9b5qZlxV3rKPcPE/oyeM1sZVsSfZTrqINNWawlnCUD9K5Vxq+OjObDecchobzsoROlsPzsga9zHvXpjmzmBkqu/EI+r9ufKFBtIsPTZZO5894AM2JYzwwHTn5AAAAAElFTkSuQmCC\" alt=\"ai\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.85px 7.79167px; transform-origin: 124.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The output should be in a similar form. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = fractDeriv(x,q)\r\n  % x = 2xn matrix with coefficients in the first row and exponents in the second row\r\n  % q = order of the derivative\r\n  % y = output matrix with coefficients in the first row and exponents in the second row\r\n  \r\n  y = q*x^(q-1);\r\nend","test_suite":"%% Example from problem description\r\nx = [1; 2];\r\nq = 1/2;\r\ny_correct = [8/(3*sqrt(pi)); 3/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Constant\r\nc = rand;\r\nx = [c; 0];\r\nq = 1/2;\r\ny_correct = [c/sqrt(pi); -1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Polynomial #1\r\nx = [3 -7 4; 2 1 0];\r\nq = 1/2;\r\ny_correct = [[8 -14 4]/sqrt(pi); 3/2 1/2 -1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10,'all'))\r\n\r\n%% Polynomial #2\r\nx = [1:4; 3:-1:0];\r\nq = 1/3;\r\ny_correct = [1.495438426033838 2.658557201837934 3.323196502297416 2.953952446486593; 8/3 5/3 2/3 -1/3];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10,'all'))\r\n\r\n%% Quadratic term\r\nx = [7; 2];\r\nq = 3/2;\r\ny_correct = [28/sqrt(pi); 1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Two fractional derivatives amounting to a first derivative\r\nq = rand;\r\nx = [6; 5];\r\nyy_correct = [30; 4];\r\nassert(all(abs(fractDeriv(fractDeriv(x,q),1-q)-yy_correct)\u003c1e-10))\r\n\r\n%% Two fractional derivatives undoing each other\r\nq = rand;\r\nx = [5; 2];\r\nassert(all(abs(fractDeriv(fractDeriv(x,q),-q)-x)\u003c1e-10))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-27T04:55:37.000Z","updated_at":"2026-01-09T18:33:26.000Z","published_at":"2021-06-27T05:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1370\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 1370\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth derivative as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^q x^a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^q x^a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then a familiar example from calculus would be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^2 x^3 = 6 x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^2 x^3 = 6 x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFractional calculus involves derivatives in which the order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is not an integer. With \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q = 1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq = 1/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^{1/2} x^2 = 8 x^{3/2} / (3 sqrt(pi))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^{1/2} x^2 = \\\\frac{8}{3\\\\sqrt{\\\\pi}} x^{3/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the fractional derivative of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of an expression of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(x) = c­1 x^a1 + c2 x^a2 + c3 x^a3 +...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = c­_1 x^{a_1} + c_2 x^{a_2} + c_3 x^{a_3} + \\\\dots \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first input to the function will be a 2x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix in which the first row is the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ci\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the second row is the exponents \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The output should be in a similar form. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52120,"title":"Compute the fractional derivative","description":"Cody Problem 1370 asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the th derivative as . Then a familiar example from calculus would be . \r\nFractional calculus involves derivatives in which the order  is not an integer. With  and , then \r\n\r\nWrite a function that computes the fractional derivative of order  of an expression of the form\r\n\r\nThe first input to the function will be a 2x matrix in which the first row is the coefficients  and the second row is the exponents . The output should be in a similar form. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 128.275px; transform-origin: 407px 128.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1370\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 1370\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.442px 7.79167px; transform-origin: 294.442px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.0083px 7.79167px; transform-origin: 49.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth derivative as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^q x^a\" style=\"width: 32px; height: 19px;\" width=\"32\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then a familiar example from calculus would be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^2 x^3 = 6 x\" style=\"width: 65.5px; height: 19px;\" width=\"65.5\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 179.725px 7.79167px; transform-origin: 179.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFractional calculus involves derivatives in which the order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.1667px 7.79167px; transform-origin: 71.1667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is not an integer. With \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"q = 1/2\" style=\"width: 51.5px; height: 18.5px;\" width=\"51.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a = 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 7.79167px; transform-origin: 19.4417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.4583px; text-align: left; transform-origin: 384px 18.4583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"D^{1/2} x^2 = 8 x^{3/2} / (3 sqrt(pi))\" style=\"width: 117px; height: 37px;\" width=\"117\" height=\"37\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 196.292px 7.79167px; transform-origin: 196.292px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the fractional derivative of order \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.675px 7.79167px; transform-origin: 88.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of an expression of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"f(x) = c­1 x^a1 + c2 x^a2 + c3 x^a3 +...\" style=\"width: 204px; height: 26px;\" width=\"204\" height=\"26\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.6333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.8167px; text-align: left; transform-origin: 384px 21.8167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.85px 7.79167px; transform-origin: 124.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first input to the function will be a 2x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.775px 7.79167px; transform-origin: 143.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix in which the first row is the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAoCAYAAAALz1FrAAAA9ElEQVRIie2VbQ2EMAyGHw9zMAMYOAUoOAc4wAEW0IAEPGABDWdh92NtRgjf2y65ZE/CDxi06du3BQqFQqEQjQVqoJXLpgz+AkZgBt5yPwAOaFIk6CTYsHquSWbAxCToJdC4cTbL2RSToJEgH7a1t3jZHldhJLjDy5UFrcIB1c1vDd559dmLI0Gqu3K8CYY4RKt40lSt5FSBmCSXmTieAYO3d5TrWkI16wZW+J6tJ90S5sqdJVCWze8kcY+vbk/vmu3tcEhFWIZXmqkrKMk+20N7mXQ7L7H8wJE6hNnWEARn6b8mi2TqxoGMjVcn3l2ohcI/8AWjzEUn2YFV5AAAAABJRU5ErkJggg==\" alt=\"ci\" style=\"width: 12.5px; height: 20px;\" width=\"12.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 7.79167px; transform-origin: 83.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the second row is the exponents \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAoCAYAAAAPOoFWAAABF0lEQVRYhe2UUQ3DIBCGPw84mAEMoGAK5qAO6mAW0FAJeJiFaqiF7aF3KWNlkJQt2cKX8FD+9n7uehx0Op1O52ewwACMgJM9J8+2pUkAZjFzgAduwF3WqYXRRYLNgEm0e6R91Cg2ux41OkfB3I5+KujVGGCRQFPmHc16YT/raka2U+e6LIgeMrqlsks1q1wgFx1mzLzjRffvjGoCBcqZa2ZvSxyX8LyjD2yZN/1fqdmF9RpMPJfZ81oFS0WX2sgssJ7cSDC9b5qZlxV3rKPcPE/oyeM1sZVsSfZTrqINNWawlnCUD9K5Vxq+OjObDecchobzsoROlsPzsga9zHvXpjmzmBkqu/EI+r9ufKFBtIsPTZZO5894AM2JYzwwHTn5AAAAAElFTkSuQmCC\" alt=\"ai\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.85px 7.79167px; transform-origin: 124.85px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The output should be in a similar form. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = fractDeriv(x,q)\r\n  % x = 2xn matrix with coefficients in the first row and exponents in the second row\r\n  % q = order of the derivative\r\n  % y = output matrix with coefficients in the first row and exponents in the second row\r\n  \r\n  y = q*x^(q-1);\r\nend","test_suite":"%% Example from problem description\r\nx = [1; 2];\r\nq = 1/2;\r\ny_correct = [8/(3*sqrt(pi)); 3/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Constant\r\nc = rand;\r\nx = [c; 0];\r\nq = 1/2;\r\ny_correct = [c/sqrt(pi); -1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Polynomial #1\r\nx = [3 -7 4; 2 1 0];\r\nq = 1/2;\r\ny_correct = [[8 -14 4]/sqrt(pi); 3/2 1/2 -1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10,'all'))\r\n\r\n%% Polynomial #2\r\nx = [1:4; 3:-1:0];\r\nq = 1/3;\r\ny_correct = [1.495438426033838 2.658557201837934 3.323196502297416 2.953952446486593; 8/3 5/3 2/3 -1/3];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10,'all'))\r\n\r\n%% Quadratic term\r\nx = [7; 2];\r\nq = 3/2;\r\ny_correct = [28/sqrt(pi); 1/2];\r\nassert(all(abs(fractDeriv(x,q)-y_correct)\u003c1e-10))\r\n\r\n%% Two fractional derivatives amounting to a first derivative\r\nq = rand;\r\nx = [6; 5];\r\nyy_correct = [30; 4];\r\nassert(all(abs(fractDeriv(fractDeriv(x,q),1-q)-yy_correct)\u003c1e-10))\r\n\r\n%% Two fractional derivatives undoing each other\r\nq = rand;\r\nx = [5; 2];\r\nassert(all(abs(fractDeriv(fractDeriv(x,q),-q)-x)\u003c1e-10))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-27T04:55:37.000Z","updated_at":"2026-01-09T18:33:26.000Z","published_at":"2021-06-27T05:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1370\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 1370\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth derivative as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^q x^a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^q x^a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then a familiar example from calculus would be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^2 x^3 = 6 x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^2 x^3 = 6 x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFractional calculus involves derivatives in which the order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is not an integer. With \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q = 1/2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq = 1/2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D^{1/2} x^2 = 8 x^{3/2} / (3 sqrt(pi))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD^{1/2} x^2 = \\\\frac{8}{3\\\\sqrt{\\\\pi}} x^{3/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the fractional derivative of order \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of an expression of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"f(x) = c­1 x^a1 + c2 x^a2 + c3 x^a3 +...\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = c­_1 x^{a_1} + c_2 x^{a_2} + c_3 x^{a_3} + \\\\dots \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first input to the function will be a 2x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix in which the first row is the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ci\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the second row is the exponents \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ai\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The output should be in a similar form. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"fractional calculus\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"fractional calculus\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"fractional calculus\"","","\"","fractional calculus","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f74ba363900\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f74ba363860\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f74ba362f00\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f74ba363d60\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f74ba363cc0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f74ba363c20\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f74ba3639a0\u003e":"tag:\"fractional calculus\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f74ba3639a0\u003e":"tag:\"fractional calculus\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"fractional calculus\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"fractional calculus\"","","\"","fractional calculus","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f74ba363900\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f74ba363860\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f74ba362f00\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f74ba363d60\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f74ba363cc0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f74ba363c20\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f74ba3639a0\u003e":"tag:\"fractional calculus\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f74ba3639a0\u003e":"tag:\"fractional calculus\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":52120,"difficulty_rating":"medium"}]}}