arXiv subjects

S. D. Roscani

Publications and source records attributed to S. D. Roscani.

2 recordsLinked to original sources

arXiv2023

On a Space Fractional Stefan problem of Dirichlet type with Caputo flux

We study a space-fractional Stefan problem with the Dirichlet boundary conditions. It is a model that describes superdiffusive phenomena. Our main result is the existence of the unique classical solution to this problem. In the proof we apply evolution operators theory and the Schauder fixed point theorem. It appears that studying fractional Stefan problem with Dirichlet boundary conditions requires a substantial modifications of the approach in comparison with the existing results for problems with different kinds of boundary conditions.

math.AP↗

arXiv2020

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

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 $E_{α,m;l}(z)$. We consider Dirichlet and Newmann 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.

math.AP↗