A solution to a one-dimensional two-phase fractional Stefan-like problem with a convective boundary conditions at the fixed face

Abstract

The text of this chapter is organized as follows: In Section 2, we will obtain the necessary condition for the coefficient which characterizes the convective boundary condition at x=0 to have an instantaneous two-phase fractional phase-change process. In Section 3, we will obtain a generalized Neumann solution for the two-phase fractional Lamé-Clapeyron-Stefan problem for a semi-infinite material with a constant initial condition, and a convective (Robin) boundary condition at the fixed face x=0 when the necessary inequality obtained in Section 2 is satisfied. When alfa goes to 1 , we also recover the Neumann solution for the classical two-phase Lamé-Clapeyron-Stefan problem through the error function when an inequality is satisfied for the coefficient that characterizes the convectiveboundary condition, which was previously obtained in (Tarzia, 2017) which is of the type given in (Tarzia 1981).