Numerical methods for solving two-dimensional nonlinear integral equations of fractional order by using two-dimensional block pulse operational matrix

Abstract

In this paper, our purpose is to construct a two-dimensional fractional integral operational matrix and its use for the numerical solution of two-dimensional fractional integral equations. We use these operational matrices and properties of two-dimensional block pulse functions (2D-BPFs), to reduce two-dimensional fractional integral equations (2D-FIEs) to a system of algebraic equations. Obtained algebraic system based on the original problem can be linear or nonlinear. Then we show convergence of the proposed methods and we find the error bounds. To show the accuracy, efficiency and speed of the proposed method linear and nonlinear examples are presented.