Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre Wavelets

Abstract

In this paper, a new general procedure of the integration operational matrix of fractional-order Legendre wavelets is presented and then used to obtain the numerical solution of fractional differential equations. The fractional derivative in these problems is in the Caputo sense. By using the operational matrix of fractional integration, the original fractional differential equation is converted into a nonlinear system of algebraic equations which can be solved by Newton’s method. The numerical results are compared with exact solutions and existing numerical solutions found in the literature and demonstrate the validity and applicability of the proposed method.