EXTREMUM PRINCIPLE FOR THE HADAMARD DERIVATIVES AND ITS APPLICATION TO NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

被引：18
|
作者：
Kirane, Mokhtar [1 ,2 ]
Torebek, Berikbol T. [3 ,4 ]
机构：
[1] Univ La Rochelle, Fac Sci, LaSIE, Pole Sci & Technol, Ave M Crepeau, F-17042 La Rochelle, France
[2] King Abdulaziz Univ, Fac Sci, Dept Math, NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia
[3] Al Farabi Kazakh Natl Univ, Al Farabi Ave 71, Alma Ata 050040, Kazakhstan
[4] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2019年 / 22卷 / 02期
关键词：
time-fractional diffusion equation; maximum principle; Hadamard derivative; fractional elliptic equation; nonlinear problem; MAXIMUM PRINCIPLE; DIFFUSION-EQUATIONS; GENERALIZED TIME; REGULARITY;
D O I：
10.1515/fca-2019-0022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：358 / 378
页数：21
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