fracinlap(u,v,a,t)

% Function to evaluate inverse laplace Transform of a fractional system
% Inverse laplace Transform of functions of the form 1/(s^u(s^v-a))
% where u and v may be fractional
% v of the form 1/q where q is any positive integer ; 1,2,3,.........n

% Input: u,v,a
% Output: y(t)

% Note the function uses the 'Riemman-Louivelle' definition for fractional integrals  

% Author : Abhirup lahiri ([e-mail])

% Example
%v=.5;
%u=1;
%t=0:.1:4;
%a=-1;

function [y]= fracinlap(u,v,a,t)

q=1/v;
a1=(a).^q;

s2=zeros(1,length(t));

for j=1:q
s1=zeros(1,length(t));
v1=j*v-1+u;
for k=0:20
    s1=s1+(a1).^k.*t.^(k+v1)./gamma(k+v1+1);      % use gamma function
end
s2=s2+(a).^(j-1).*s1;
end

y=s2;
%plot(t,y)
%grid