Application of the collocation method for solving nonlinear fractional integro-differential equations

In this paper, using the collocation method we solve the nonlinear fractional integro-differential equations (NFIDE) of the form: f(t,y(t),aCDtα0y(t),…,aCDtαry(t))=λG(t,y(t),∫atk(t,s)F(s,y(s))ds),y(k)(a)=dk,y(k)(a)=dk,k=0,1,…,m0−1.k=0,1,…,m0−1. We study the convergence and the stability analysis of this method for f(t,y(t),aCDtα0y(t),…,aCDtαry(t))=y(t)+∑j=0rbjaCDtαjy(t)+g(t). Some numerical examples are given to show the efficiency of the presented method.