  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.
