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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

IMPACT FACTOR 2018: 3.514
5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891
Source Normalized Impact per Paper (SNIP) 2018: 1.808

Mathematical Citation Quotient (MCQ) 2018: 1.08

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Volume 22, Issue 2


Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations

Mokhtar Kirane
  • LaSIE, Faculté des Sciences, Pole Sciences et Technologies, Université de La Rochelle, Avenue M. Crepeau 17042, La Rochelle Cedex, France
  • NAAM Research Group, Department of Mathematics Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
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/ Berikbol T. Torebek
  • Al–Farabi Kazakh National University, Al–Farabi ave. 71, 050040, Almaty, Kazakhstan
  • Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., 050010, Almaty, Kazakhstan
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Published Online: 2019-05-11 | DOI: https://doi.org/10.1515/fca-2019-0022


In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear time-fractional diffusion equations possesses at most one classical solution and this solution depends continuously on the initial and boundary conditions. The extremum principle for an elliptic equation with a fractional Hadamard derivative is also proved.

MSC 2010: Primary 35B50; Secondary 26A33; 35K55; 35J60

Key Words and Phrases: time-fractional diffusion equation; maximum principle; Hadamard derivative; fractional elliptic equation; nonlinear problem


About the article

Received: 2018-06-05

Published Online: 2019-05-11

Published in Print: 2019-04-24

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 2, Pages 358–378, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0022.

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