A new equivalence of Stefan’s problems for the time fractional diffusion equation

Abstract

A fractional Stefan’s problem with a boundary convective condition is solved, where the fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. Then an equivalence with other two fractional Stefan’s problems (the first one with a constant condition on x = 0 and the second with a flux condition) is proved and the convergence to the classical solutions is analyzed when α 1 recovering the heat equation with its respective Stefan’s condition