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We study a space-fractional Stefan problem with the Dirichlet boundaryconditions. It is a model that describes superdiffusive phenomena. Our mainresult is the existence of the unique classical solution to this problem. Inthe proof we apply evolution operators theory and the Schauder fixed pointtheorem. It appears that studying fractional Stefan problem with Dirichletboundary conditions requires a substantial modifications of the approach incomparison with the existing results for problems with different kinds ofboundary conditions.

On a Space Fractional Stefan problem of Dirichlet type with Caputo flux