A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation

Abstract

A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $\alpha \in (0,1)$ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first one with a constant condition on $x=0$ and the second with a flux condition)is proved and the convergence to the classical solutions is analyzed when $\alpha \nearrow 1$ recovering the heat equation with its respective Stefan condition.

This paper was already accepted to be published in the in the journal "Fractional Calculus and Applied Analysis". arXiv admin note: substantial text overlap with arXiv:1306.1750

References in corpus (1)

• Two equivalent Stefan's problems for the Time Fractional Diffusion Equation

Cited by in corpus (3)

• Determination of two unknown thermal coefficients through an inverse one-phase fractional Stefan problem
• A note on models for anomalous phase-change processes
• An integral Relationship for a new Fractional One-phase Stefan Problem