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arXiv · 2009.12977

The similarity method and explicit solutions for the fractional space one-phase Stefan problems

S. D. Roscani·D. A. Tarzia·L. Venturato
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Abstract

In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space one-phase Stefan problem in terms of the three parametric Mittag-Leffer function $E_{\alpha,m;l}(z)$. We consider Dirichlet and Newmann conditions at the fixed face, involving Caputo fractional space derivatives of order $0 < \alpha < 1$. We recover the solution for the classical one-phase Stefan problem when the order of the Caputo derivatives approaches one.

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S. D. Roscani, D. A. Tarzia, L. Venturato. 2020-09-27. The similarity method and explicit solutions for the fractional space one-phase Stefan problems. https://arxiv.org/abs/2009.12977

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