On a Space Fractional Stefan Problem of Dirichlet Type With Caputo Flux

ABSTRACT We study a space‐fractional Stefan problem with Dirichlet boundary conditions, which models superdiffusive phenomena. Our main result is the existence of the unique classical solution to this problem. In the proof we apply the theory of evolution operators and the Schauder fixed‐point theorem. It appears that studying fractional Stefan problem with Dirichlet boundary conditions requires substantial modifications of the approach in comparison with the existing results for problems with different kinds of boundary conditions.