An efficient numerical method for two-dimensional fractional integro-differential equations with modified Atangana–Baleanu fractional derivative using operational matrix approach

Abstract

In the present paper, a numerical method is developed for solving non-homogeneous two-dimensional fractional integro-differential equations with a modified Atangana–Baleanu fractional derivative. The approach is based on the operational matrix method, involving the derivation of operational matrices for the terms of the equation to generate an algebraic system that is solved using mathematical software. First, basic definitions of fractional calculus and block pulse functions are presented. Then, the operational matrices and the method of solution are derived. The existence and uniqueness of the solution of the proposed equation are proved. Examples to test the numerical method are provided, demonstrating the efficiency of the proposed method.