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arXiv · 1801.08904

Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions

Meiirkhan Borikhanov·Mokhtar Kirane·Berikbol T. Torebek
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Abstract

In this paper, a maximum principle for the one-dimensional sub-diffusion equation with Atangana-Baleanu fractional derivative is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Atangana-Baleanu fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the linear and nonlinear time-fractional diffusion equations possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions.

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Meiirkhan Borikhanov, Mokhtar Kirane, Berikbol T. Torebek. 2018-01-26. Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions. https://arxiv.org/abs/1801.08904

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