An integral Relationship for a new Fractional One-phase Stefan Problem

TL;DR

This paper introduces a new integral relationship for a fractional one-phase Stefan problem, providing an exact similarity solution involving Wright functions, advancing the mathematical understanding of phase change problems with fractional derivatives.

Contribution

It derives an integral relationship equivalent to the fractional Stefan condition and presents an exact similarity solution using Wright functions.

Findings

Derived an integral relationship for the fractional Stefan problem.

Obtained an exact similarity solution in terms of Wright functions.

Enhanced mathematical framework for fractional phase change problems.

Abstract

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered. An integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is given.