Two equivalent Stefan’s problems for the time fractional diffusion equation

Abstract

Two Stefan’s problems for the diffusion fractional equation are solved, where the fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. The first one has a constant condition on x = 0 and the second presents a flux condition Tx(0, t) = q t α/2. An equivalence between these problems is proved and the convergence to the classical solutions is analyzed when α 1 recovering the heat equation with its respective Stefan’s condition.