Perturbed least squares technique for solving Volterra fractional integro-differential equations based on constructed orthogonal polynomials

Abstract

A numerical method is presented in this paper to solve fractional integro-differential equations in the sense of Caputo, the fractional derivative is considered. The proposed method is perturbed Least Squares Method (PLSM) with the aid of constructed orthogonal polynomials as basis functions. The suggested method reduces this type of problem to a solution of system of linear algebraic equations and then solved using Maple 18 software. Some numerical examples are provided to show the accuracy and applicability of the presented method, numerical results show that when applied to fractional integro-differential equations, the method is easy to implement and accurate.