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

2018/01/26 by Borikhanov, Meiirkhan, Kirane, Mokhtar, Torebek, Berikbol T.
#26A33 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08904

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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