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

Abstract

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.