Analytical methods for solving time-fractional Stefan problem for diffusion-convection-reaction equation

Abstract

This study investigates a time-fractional Stefan problem that models phase-change processes in media exhibiting anomalous diffusion and memory effects. A fractional Stefan model with an advective–diffusive flux is developed by deriving the Stefan condition from the time-fractional diffusion–convection–reaction equation. A rescaling technique reduces the original fractional PDE to a self-similar form that enables deeper analytical exploration. The interface function is constructed to satisfy boundary and Stefan conditions. Approximate solutions are obtained using fractional derivatives in the Riemann–Liouville and Caputo formulations. The model is applicable to heat transport in porous media, cryosurgery, groundwater contamination, and thermal energy storage.