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arXiv · 1306.1750

Two equivalent Stefan's problems for the Time Fractional Diffusion Equation

Sabrina Roscani·Eduardo A. Santillan Marcus
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Abstract

Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order $ \al \in (0,1) $ is taken in the Caputo's sense. The first one has a constant condition on $ x = 0 $ and the second presents a flux condition $ T_x (0, t) = \frac {q} {t ^ {\al/2}} $. An equivalence between these problems is proved and the convergence to the classical solutions is analysed when $ \al \nearrow $ 1 recovering the heat equation with its respective Stefan's condition.

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Sabrina Roscani, Eduardo A. Santillan Marcus. 2013-06-07. Two equivalent Stefan's problems for the Time Fractional Diffusion Equation. https://doi.org/10.2478/s13540-013-0050-7

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