# FRB

## Seminar

### Generalized Neumann solutions for the two-phase fractional Lam\'e-Clapeyron-Stefan problems

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

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 is obtained. In this problem, the two governing diffusion equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order 0Moreover, we also obtain a new generalized Neumann solutions for the two-phase fractional Lam\'e-Clapeyron-Stefan problems when a heat flux or a convective boundary condition is imposed on the fixed face x=0. These solutions are obtained when an inequality for the coefficient which characterizes the heat flux or the convective boundary condition is satisfied. In these cases, when a? 1 we also recover the explicit solution given in Tarzia, Quart. Appl. Math., 39 (1981), 491-499 and in MAT-Serie A, 8 (2004), 21-27.

The first part of this presentation is a joint work with S.D. Roscani (Univ. Rosario, Argentina).

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