On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations

Abstract

An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear or nonlinear weakly singular Volterra–Fredholm integral equation. In order to solve this integral equation, after a brief introduction of Müntz–Legendre wavelets, and representing the fractional integral operator as a matrix, we apply the wavelet collocation method to obtain a system of nonlinear or linear algebraic equations. An a posteriori error estimate for the method is investigated. The numerical results confirm our theoretical analysis, and comparing the method with existing ones demonstrates its ability and accuracy.