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Zbl 1201.80065
Voller, V.R.
An exact solution of a limit case Stefan problem governed by a fractional diffusion equation.
(English)
[J] Int. J. Heat Mass Transfer 53, No. 23-24, 5622-5625 (2010). ISSN 0017-9310

Summary: An anomalous diffusion version of a limit Stefan melting problem is posed. In this problem, the governing equation includes a fractional time derivative of order $0 < \beta \leqslant 1$ and a fractional space derivative for the flux of order $0 < \alpha \leqslant 1$. Solution of this fractional Stefan problem predicts that the melt front advance as $s = t^{\gamma}, \gamma = \frac {\beta}{\alpha+1}$. This result is consistent with fractional diffusion theory and through appropriate choice of the order of the time and space derivatives, is able to recover both sub-diffusion and super-diffusion behaviors for the melt front advance.
MSC 2000:
*80A22 Stefan problems, etc.
26A33 Fractional derivatives and integrals (real functions)

Keywords: Stefan problem; anomalous diffusion; fractional derivative

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