A block pulse operational matrix method for solving two-dimensional nonlinear integro-differential equations of fractional order

In this paper, we use two-dimensional block pulse functions (2D-BPFs) and their operational matrix for integration and fractional integration, to reduce two-dimensional fractional integro-differential equations (2D-FIDEs) to a system of nonlinear algebraic equations. The solution is determined by solving this system. Also by two theorems, we prove the convergence of the proposed method. Finally, the numerical solutions guarantee the desired accuracy and efficiency.