A space-fractional Stefan problem

TL;DR

This paper investigates a space-fractional Stefan problem involving non-local diffusion modeled by the Caputo derivative, establishing the existence and uniqueness of classical solutions.

Contribution

It introduces a novel space-fractional Stefan problem with Caputo derivative diffusion and proves the unique existence of classical solutions.

Findings

Existence of unique classical solutions

Modeling non-local diffusion with Caputo derivative

Advancement in fractional Stefan problems

Abstract

We study a space-fractional Stefan problem, where the non-local diffusion flux is modeled by the Caputo derivative. We obtain the unique existence of classical solution to this problem.