Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel

摘要

In this paper, numerical solutions of the linear and nonlinear fractional integro- differential equations with weakly singular kernel where fractional derivatives are considered in the Ca-puto sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration for Legendre wavelets. The application of this matrix for solving initial problem is explained. The mentioned equations are transformed into a system of algebraic equations. The error analysis of the proposed method is investigated. Finally, some numerical examples are shown to illustrate the efficiency of the approach.