A Generalized Neumann Solution for the Two-Phase Fractional Lam\'{e}-Clapeyron-Stefan Problem

Abstract

We obtain a generalized Neumann solution for the two-phase fractional Lam\'{e}-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order $0<\al\leq 1$. When $ \al \nearrow $ 1 we recover the classical Neumann solution for the two-phase Lam\'{e}-Clapeyron-Stefan problem given through the error function.