In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space Stefan problem in terms of the three parametric Mittag-Leffler function \(E_{\alpha ,m,l}(z)\). We consider Dirichlet and Neumann 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.

中文翻译：

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分数空间一相Stefan问题的相似方法及显式解

在本文中，我们根据三参数 Mittag-Leffler 函数\(E_{\alpha ,m,l}(z)\)获得一相一维分数空间 Stefan 问题的自相似解。我们考虑固定面的 Dirichlet 和 Neumann 条件，涉及阶\(0<\alpha <1\)的 Caputo 分数空间导数。当 Caputo 导数的阶数接近 1 时，我们恢复了经典单相 Stefan 问题的解。