Two-dimensional advection-diffusion process with memory and concentrated source

Abstract

Two-dimensional advection-diffusion processeswithmemory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studiedmodel is a fractional differential equation with short-tail memory (a differential equation with Caputo-Fabrizio time-fractional derivatives). An analytical solution of the initial-boundary value problem has been determined by employing the Laplace transform and double sine-Fourier transforms. A numerical solution of the studied problem has been determined using finite difference approximations. Numerical simulations for both solutions have been carried out using the software Mathcad.