Legendre wavelets method for solving fractional integro-differential equations

In this paper, based on the constructed Legendre wavelets operational matrix of integration of fractional order, a numerical method for solving linear and nonlinear fractional integro-differential equations is proposed. By using the operational matrix, the linear and nonlinear fractional integro-differential equations are reduced to a system of algebraic equations which are solved through known numerical algorithms. The upper bound of the error of the Legendre wavelets expansion is investigated in Theorem 5.1. Finally, four numerical examples are shown to illustrate the efficiency and accuracy of the approach.