A cardinal approach for two-dimensional modified anomalous space–time fractional sub-diffusion equation

Abstract

In this paper, the modified anomalous space–time fractional sub-diffusion equation in two dimensions is introduced. The Chebyshev cardinal polynomials (as an appropriate family of basis functions) are successfully used to make a computational technique for this equation. To this end, the time and space fractional derivative matrices of these polynomials are obtained at first. Then, by approximating the unknown solution via the expressed polynomials and applying these matrices, as well as the collocation technique, solving the problem turns into solving an algebraic system of equations. The capability of the approach is checked by solving two test problems.