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arXiv · 1402.2191

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

Sabrina Roscani·Eduardo Santillan Marcus
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Abstract

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.

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Sabrina Roscani, Eduardo Santillan Marcus. 2014-02-10. A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation. https://doi.org/10.2478/s13540-014-0175-3

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