Numerical solution of a non-local fractional convection-diffusion equation

This article investigates the numerical solutions of a fractional non -local convection-diffusion equation in time, defined in the Caputo sense. The approximations are developed using an explicit numerical scheme through the finite difference method. Through this discretization and the Von Neumann method, the Courant-Friedrichs-Lewy (CFL) stability condition is established, which demonstrates the monotonicity property and the total variation diminishing (TVD) property, along with some important inequalities for the regularity of the scheme. Finally, some numerical experiments with a source term are presented to find analytical solutions and perform the respective error calculations and convergence orders with the numerical approximation.