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 T x (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.
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Roscani, S., Marcus, E.S. Two equivalent Stefan’s problems for the time fractional diffusion equation. fcaa 16, 802–815 (2013). https://doi.org/10.2478/s13540-013-0050-7
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DOI: https://doi.org/10.2478/s13540-013-0050-7