Solución Numérica de una ecuación de convección-difusión no local fraccionaria

In this paper we consider a non-local time-fractional convection-diffusion equation. The fractional derivative is defined in the Caputo sense. The numerical solution is developed by an explicit numerical scheme using the finite differences method and discrete mollification for the non-local term. From the numerical scheme and the von Neumann method, the stability condition (CFL) is established. The monotony property, the total variation property (TVD) and some important inequalities in the regularity of the scheme are proved using the stability condition. Finally, some numerical experiments with a source term are presented, which allows finding the analytical solutions to perform the respective calculations of the errors and convergence orders with the numerical approximation.