A numerical method for the solution of the two-phase fractional Lame-Clapeyron-Stefan problem

Abstract

In this paper we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative procedure, which allows us to determine the position of the moving boundary. In the final part, we also present some examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.