Sabrina Roscani, Julieta Bollati, Domingo Tarzia
Published 2018-05-23Version 1
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered. The model obtained involves fractional derivatives with respect on time in the sense of Caputo and in the sense of Riemann--Liouville. An integral relationship for the free boundary which is equivalent to the `fractional Stefan condition' is also obtained.
Comments: 26 pages, 2 figures
Explicit solution for Stefan problem with latent heat depending on the position and a convective boundary condition at the fixed face using Kummer functions
An integral Relationship for a new Fractional One-phase Stefan Problem
Cascade equation for the discontinuities in the Stefan problem with surface tension
![QR code for arXiv:1805.09115 [math.AP]](http://oss.arxitics.com/images/favicon.svg)