Numerical algorithm to solve fractional integro-differential equations based on Legendre wavelets method

The purpose of this paper is to study the Legendre wavelets for the solution of linear and nonlinear fractional integro-differential equations. The properties of Legendre wavelets together with the fractional order operational matrix of integration are used to reduce the problem to the solution of a system of algebraic equations. Also a reliable approach for convergence of the Legendre wavelets method is discussed. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution.