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arXiv · 1806.04886

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

Mokhtar Kirane·Berikbol T. Torebek
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Abstract

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.

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Mokhtar Kirane, Berikbol T. Torebek. 2018-06-13. Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations. https://doi.org/10.1515/fca-2019-0022

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