A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation

A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $\alpha \in (0,1)$ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan 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 $\alpha \nearrow 1$ recovering the heat equation with its respective Stefan condition.