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A note on models for anomalous phase-change processes

  • Andrea N. Ceretani EMAIL logo


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.


The author thanks Roberto Garra (La Sapienza, Rome, Italy), Federico Falcini (Consiglio Nazionale delle Ricerche, Rome, Italy), Vaughan Voller (University of Minnesota, Minneapolis, USA), Domingo Tarzia (Universidad Austral - CONICET, Rosario, Argentina), and Sabrina Roscani (Universidad Austral - CONICET, Rosario, Argentina) for fruitful discussions. She also thanks the anonymous referee, whose valuable comments have helped improve the original manuscript.

This work has been partially supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) of Argentina within a Postdoctoral Grant at Universidad Austral, Rosario, Argentina.


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Received: 2018-06-01
Revised: 2019-11-25
Published Online: 2020-02-27
Published in Print: 2020-02-25

© 2020 Diogenes Co., Sofia

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