Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions

Abstract

This paper presents hybrid of rationalized Haar (HRH) functions method for approximate the numerical solution of the fractional nonlinear Fredholm integro-differential equations (FNFIDEs). The fractional derivatives are considered in the sense of Caputo. The fractional operational matrix of hybrid of block-pulse and rationalized Haar functions are presented. This matrix together with the dual operational matrix are used to reduce the computation of FNFIDEs into a system of algebraic equations. Some numerical examples are given and the results of applying this method demonstrate time and computational are small.