Developing the discretization method for fractal‐fractional two‐dimensional Fredholm–Volterra integro‐differential equations

Abstract

This paper contains the computational approach based on Mott polynomials together with the two‐dimensional Legendre–Gauss (LG) quadrature rule for fractal‐fractional two‐dimensional Fredholm–Volterra (FF‐2D‐FV) integro‐differential equations. Furthermore, we applied the modified operational matrices of integration and fractional derivative in the process of the numerical algorithm to get the approximate solution with high accuracy. The fractal‐fractional derivative is defined in the Atangana–Riemann–Liouville sense. Besides, we estimate the error of the method in Sobolev space. Ultimately, to prove the theoretical claim, we represent the numerical results in the form of tables and diagrams.