English

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

Analysis of PDEs 2019-10-22 v1

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.

Keywords

Cite

@article{arxiv.1806.04886,
  title  = {Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations},
  author = {Mokhtar Kirane and Berikbol T. Torebek},
  journal= {arXiv preprint arXiv:1806.04886},
  year   = {2019}
}