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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 14, Issue 1

Issues

Maximum principle and its application for the time-fractional diffusion equations

Yury Luchko
  • Department of Mathematics II, Beuth University of Applied Sciences Berlin, Luxemburger Str. 10, 13353, Berlin, Germany
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Published Online: 2011-01-15 | DOI: https://doi.org/10.2478/s13540-011-0008-6

Abstract

In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative, the Caputo fractional derivative is shown to possess a suitable generalization of the extremum principle well-known for ordinary derivative. As an application, the maximum principle is used to get some a priori estimates for solutions of initial-boundary-value problems for the generalized time-fractional diffusion equations and then to prove uniqueness of their solutions.

MSC: 26A33; 33E12; 35B45; 35B50; 35K99; 45K05

Keywords: time-fractional diffusion equation; time-fractional multi-term diffusion equation; time-fractional diffusion equation of distributed order; extremum principle; Caputo fractional derivative; generalized Riemann-Liouville fractional derivative; initial-boundary-value problems; maximum principle; uniqueness results

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About the article

Published Online: 2011-01-15

Published in Print: 2011-03-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 14, Issue 1, Pages 110–124, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-011-0008-6.

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© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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