Solve a integral equation

I would like to solve this equation in MATLAB

,

we know and and

[Saranya S]

Program for ZTransform

x= [9 2 3 4 5];

b=0;

n= length(x);

y=sym('Z');

for i=1:n

b=b+x(i)*y^(1-i);

end

display(b);

[Saranya S]

syms t s;

f=-1.25+3.5*t*exp(-2*t)+1.25*exp(-2*t)

f =

(5*exp(-2*t))/4 + (7*t*exp(-2*t))/2 - 5/4

f=laplace(f);

simplify(f);

pretty(ans)

[Saranya S]

Fourier Transform

syms a t;

x= a*abs(t);

x= fourier(x);

x1= fourier(x,y);

x2=fourier(x,t,y);

disp('1.Fourier Transform of a*abs:')

disp(x);

disp(x1);

disp(x2);

Answer 1

[Walter Roberson]

Q = @(v) sym(v);

syms t C real
alpha = Q(2);
sigma = Q(0.4);
Pi = Q(pi);

f(t) = exp(-(log(t)^2/(2*sigma^2)))/(t * sigma * sqrt(2*Pi))

f(t) = 

eqn = C - int((t-alpha*C)*f(t), t, alpha*C, inf)

eqn = 

SE = simplify(eqn)

SE = 

C_sol = vpasolve(SE, C)

C_sol = 

0.3721630585289762803836642354681

subs(eqn, C, C_sol)

ans = 

vpa(ans)

ans =