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

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 Caputo 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.