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.

引用

页码：358 / 378

页数：21

共 50 条

[1] Extremum Principle for the Hadamard Derivatives and Its Application to Nonlinear Fractional Partial Differential Equations
Mokhtar Kirane
Berikbol T. Torebek
Fractional Calculus and Applied Analysis, 2019, 22 : 358 - 378
[2] Maximum principle for Hadamard fractional differential equations involving fractional Laplace operator
Wang, Guotao
Ren, Xueyan
Baleanu, Dumitru
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (05) : 2646 - 2655
[3] Maximum Principle for Space and Time-Space Fractional Partial Differential Equations
Kirane, Mokhtar
Torebek, Berikbol T.
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2021, 40 (03): : 277 - 301
[4] Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative
Elbukhari, Abu Bakr
Fan, Zhenbin
Li, Gang
FRACTAL AND FRACTIONAL, 2023, 7 (07)
[5] Maximum Principle and Application of Parabolic Partial Differential Equations
Dong Fangliang
2012 INTERNATIONAL CONFERENCE ON MECHANICAL AND ELECTRONICS ENGINEERING, 2012, 3 : 198 - 205
[6] Asymptotic Behavior of Solutions of Nonlinear Fractional Differential Equations with Caputo-Type Hadamard Derivatives
John R. Graef
Said R. Grace
Ercan Tunç
Fractional Calculus and Applied Analysis, 2017, 20 : 71 - 87
[7] ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH CAPUTO-TYPE HADAMARD DERIVATIVES
Graef, John R.
Grace, Said R.
Tunc, Ercan
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (01) : 71 - 87
[8] THE MAXIMUM PRINCIPLE FOR TIME-FRACTIONAL DIFFUSION EQUATIONS AND ITS APPLICATION
Brunner, Hermann
Han, Houde
Yin, Dongsheng
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2015, 36 (10) : 1307 - 1321
[9] Maximum principle and its application for the time-fractional diffusion equations
Yury Luchko
Fractional Calculus and Applied Analysis, 2011, 14 : 110 - 124
[10] MAXIMUM PRINCIPLE AND ITS APPLICATION FOR THE TIME-FRACTIONAL DIFFUSION EQUATIONS
Luchko, Yury
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2011, 14 (01) : 110 - 124

← 1 2 3 4 5 →