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A Note on Models for Anomalous Phase-Change Processes

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Abstract

We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo’s definition. We survey the assumptions from which they are obtained and observe that the problems are nonequivalent though all of them reduce to a classical Stefan problem when the order of the fractional derivatives is replaced by one. We further show that a simple heuristic approach built upon a fractional version of the energy balance and the classical Fourier’s law leads to a natural generalization of the classical Stefan problem in which time derivatives are replaced by fractional ones.

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Authors and Affiliations

  1. IMAS-UBA-CONICET Intendente Guiraldes 2160, Capital Federal, 1428, Argentina

    Andrea N. Ceretani

  2. Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, Martín de Irigoyen 3100, San Martín, 1650, Argentina

    Andrea N. Ceretani

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Ceretani, A.N. A Note on Models for Anomalous Phase-Change Processes. Fract Calc Appl Anal 23, 167–182 (2020). https://doi.org/10.1515/fca-2020-0006

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