A Generalized Neumann Solution for the Two-Phase Fractional Lamé-Clapeyron-Stefan Problem

Abstract

We obtain a generalized Neumann solution for the two-phase fractional Lamé-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 Lamé-Clapeyron-Stefan problem given through the error function.

13 pages, 2 figures

References in corpus (2)

• The fundamental solution of the space-time fractional diffusion equation
• Analytical properties and applications of the Wright function