An effective scheme for solving system of fractional Volterra–Fredholm integro-differential equations based on the Müntz–Legendre wavelets

Abstract

In this study, a class of wavelet techniques is used for finding approximate solutions of systems of fractional integro-differential Volterra–Fredholm (FIDVF) equations based on the Müntz–Legendre wavelets (MLW). For the suggested method, operational matrices of the Riemann–Liouville fractional (RLF) integral and Caputo fractional (CF) derivative operators are obtained and used for converting the system of the integral equations into a system of linear or nonlinear algebraic equations. Using the Lipschitz’s condition for multivariate functions and the fixed point theorem, the existence and uniqueness of the solution are shown and also convergence, stability and error bound of the solution in interval 0,1 are investigated in this work. At the end, three examples are indicated and the results of the proposed method are compared with the first and second kind wavelet Chebyshev methods.