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

ROSCANI, SABRINA D.; TARZIA, DOMINGO A.; VENTURATO, LUCAS D.

Fractional Calculus and Applied Analysis

Springer Nature

Año: 2022 vol. 25 p. 995 - 1021

1311-0454

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 Eα,m,l(z). We consider Dirichlet and Neumann conditions at the fixed face, involving Caputo fractional space derivatives of order 0 < α< 1. We recover the solution for the classical one-phase Stefan problem when the order of the Caputo derivatives approaches one.