FDDE_PI1_Ex

Solving nonlinear fractional delay differential equations (FDDEs) with one constant delay

Solves a nonlinear fractional delay differential equation (FDDE) with one constant delay tau > 0 in the form

D^alpha y(t) = g(t, y(t), y(t-tau))
y(t) = phi(t) t0-tau <= t <= t0

where D^alpha is the fractional Caputo derivative of order 0 < alpha < 1.

As initial data it must be provided not just a single value but a whole function phi(t) for t in the interval [t0-tau, t0].

The FDDE is solved by an explicit rectangular Product-Integration (PI) scheme suitably modified to solve FDEs with one constant delay.

Usage [t, y] = FDDE_PI1_Ex(alpha,g,tau,t0,T,phi,h)

Further information about this code are available in the Section 6 of the paper [1]; please, cite this code as [1].

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Description of input parameters
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alpha : fractional order of the delay differential equation; it must be 0 < alpha < 1
g : function handle evaluating the vector field g(t,y(t),y(t-tau))
tau : constant delay; it must be tau > 0
t0, T : starting and final time of the interval of integration
phi : function handle for the initial data phi(t)
h : integration step-size; it must be selected such that h <= tau

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References and other information
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[1] Garrappa R., Kaslik E.: On initial conditions for fractional delay differential equations, Communications in Nonlinear Science and Numerical Simulation, 2020, 90, 105359, doi: 10.1016/j.cnsns.2020.105359

Author: Roberto Garrappa (University of Bari, Italy)
Homepage: https://www.dm.uniba.it/members/garrappa

Please, report any problem or comment to : roberto dot garrappa at uniba dot it