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Licensed Unlicensed Requires Authentication Published by De Gruyter May 11, 2019

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

  • Mokhtar Kirane EMAIL logo and Berikbol T. Torebek


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.


The second author was financially supported by a Grant No. AP05131756 from the Ministry of Science and Education of the Republic of Kazakhstan. No new data was collected or generated during the course of research.


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Received: 2018-06-05
Published Online: 2019-05-11
Published in Print: 2019-04-24

© 2019 Diogenes Co., Sofia

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