A new mathematical formulation for a phase change problem with a memory flux

A mathematical formulation for a one-phase change problem in a form of Stefan problem with a memory flux is obtained. The hypothesis that the integral of weighted backward fluxes is proportional to the gradient of the temperature is considered. The model that arises involves fractional derivatives with respect to time both in the sense of Caputo and of Riemann-Liouville. An integral relation for the free boundary, which is equivalent to the “fractional Stefan condition”, is also obtained.