A note about fractional Stefan problem

TL;DR

This paper introduces a fractional version of the one-phase Stefan problem by incorporating a time-fractional Riemann-Liouville derivative to model memory effects in diffusion.

Contribution

It derives a novel fractional Stefan model that accounts for memory effects using fractional calculus, extending classical Stefan problems.

Findings

Formulation of the fractional Stefan problem with Riemann-Liouville derivative

Mathematical analysis of the model's properties

Potential applications in anomalous diffusion processes

Abstract

We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we impose the memory effect in the examined model.