A note on models for anomalous phase-change processes

Author:

Ceretani Andrea N.12

Affiliation:

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

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Fractional Stefan Problem: A Survey of the Recent Results;Lobachevskii Journal of Mathematics;2023-08

2. Fractional Stefan Problem Solving by the Alternating Phase Truncation Method;Symmetry;2022-11-01

3. Mesh scheme for a phase transition problem with time-fractional derivative;Russian Journal of Numerical Analysis and Mathematical Modelling;2022-06-01

4. A self‐similar solution to time‐fractional Stefan problem;Mathematical Methods in the Applied Sciences;2020-11-16

5. Explicit solutions to fractional Stefan-like problems for Caputo and Riemann–Liouville derivatives;Communications in Nonlinear Science and Numerical Simulation;2020-11

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