Numerical approximation of the space-time fractional diffusion problem

Fractional differential equations have become central tools for the accurate modeling of real-world phenomena in various fields. This work focuses on the discretization of the space-time fractional diffusion problem with Caputo derivative in time and Riesz-Caputo derivative in space. We introduce a collocation method based on a B-spline representation of the solution. This approach strategically exploits the symmetry properties of both the spline basis functions and the Riesz-Caputo operator, resulting in an efficient method for solving the given fractional differential problem. Preliminary numerical tests are presented to validate the proposed collocation method. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)