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

TL;DR

This paper investigates a space-fractional Stefan problem with Dirichlet boundary conditions, establishing the existence and uniqueness of classical solutions for a model describing superdiffusive phenomena using advanced mathematical tools.

Contribution

It introduces a novel approach to solving fractional Stefan problems with Dirichlet conditions, requiring significant modifications from existing methods for other boundary types.

Findings

Proves existence of unique classical solutions

Uses evolution operators and Schauder fixed point theorem

Highlights the need for modified approaches for Dirichlet conditions

Abstract

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