Bernstein Least-Squares Technique for solving fractional Integro-Differential Equations

Abstract

In this paper, a numerical technique for solving fractional Integro-Differential Equations (FIDEs) is presented. The fractional derivative is considered in the Caputo sense. The proposed method is Bernstein Least- Squares Technique (BLST) via Bernstein polynomials as basis functions. The suggested new technique reduced this type of problem to the solution of a system of linear algebraic equations and then solved using MAPLE 18. To demonstrate the accuracy and applicability of the presented method, some numerical problems are provided. Numerical results show that the method is easy to implement and accurate when applied to FIDEs. The graphical solution of the method is displayed.