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 $α\in (0,1)$ 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 $α\nearrow 1$ recovering the heat equation with its respective Stefan condition.

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