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Fractional Calculus and Applied Analysis

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A new equivalence of Stefan’s problems for the time fractional diffusion equation

Sabrina Roscani
  • Departamento de Matemática — ECEN Facultad de Cs. Exactas, Ingeniería y Agrimensura Universidad Nacional de Rosario, Av. Pellegrini 250, 2000, Rosario, Argentina
  • Email:
/ Eduardo Marcus
  • Departamento de Matemática Facultad de Cs. Empresariales, Universidad Austral Rosario, Paraguay 1950, 2000, Rosario, Argentina
  • Email:
Published Online: 2014-03-21 | DOI: https://doi.org/10.2478/s13540-014-0175-3

Abstract

A fractional Stefan’s problem with a boundary convective condition is solved, where the fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. Then an equivalence with other two fractional Stefan’s problems (the first one with a constant condition on x = 0 and the second with a flux condition) is proved and the convergence to the classical solutions is analyzed when α ↗ 1 recovering the heat equation with its respective Stefan’s condition.

MSC: Primary 26A33; Secondary 33E12, 35R11, 35R35, 80A22

Keywords: Caputo’s fractional derivative; fractional diffusion equation; Stefan’s problem

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About the article

Published Online: 2014-03-21

Published in Print: 2014-06-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0175-3. Export Citation

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