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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 36, Issue 2


Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications

Mohammed Al-Refai
  • Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates
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/ Yuri Luchko
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  • Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences, Luxemburger Str. 10, 13353 Berlin, Germany
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Published Online: 2015-08-28 | DOI: https://doi.org/10.1515/anly-2015-5011


In this paper, we formulate and prove the weak and strong maximum principles for a general parabolic-type fractional differential operator with the Riemann–Liouville time-fractional derivative of distributed order. The proofs of the maximum principles are based on an estimate of the Riemann–Liouville fractional derivative at its maximum point that was recently derived by the authors. Some a priori norm estimates for solutions to initial-boundary value problems for linear and nonlinear fractional diffusion equations of distributed order and uniqueness results for these problems are presented.

Keywords: Riemann–Liouville fractional derivative; distributed-order time-fractional diffusion equation; initial-boundary value problems; maximum principle; uniqueness theorem; stability; linear equation of distributed order; nonlinear equation of distributed order

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

About the article

Received: 2015-06-24

Accepted: 2015-07-26

Published Online: 2015-08-28

Published in Print: 2016-05-01

Citation Information: Analysis, Volume 36, Issue 2, Pages 123–133, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2015-5011.

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