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

[41] Recent advances in numerical methods for partial fractional differential equations
Podlubny, Igor
Skovranek, Tomas
Datsko, Bohdan
2014 15TH INTERNATIONAL CARPATHIAN CONTROL CONFERENCE (ICCC), 2014, : 454 - 457
[42] Domain decomposition methods for space fractional partial differential equations
Jiang, Yingjun
Xu, Xuejun
JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 350 : 573 - 589
[43] The Maximum Principle for Variable-Order Fractional Diffusion Equations and the Estimates of Higher Variable-Order Fractional Derivatives
Xue, Guangming
Lin, Funing
Su, Guangwang
FRONTIERS IN PHYSICS, 2020, 8
[44] Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
Li Kexue
Peng Jigen
Jia Junxiong
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (02) : 476 - 510
[45] On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Glatt-Holtz, Nathan
Mattingly, Jonathan C.
Richards, Geordie
JOURNAL OF STATISTICAL PHYSICS, 2017, 166 (3-4) : 618 - 649
[46] Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives
Al-Refai, Mohammed
Luchko, Yuri
APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 40 - 51
[47] Numerical approximation and error analysis for Caputo-Hadamard fractional stochastic differential equations
Yang, Zhiwei
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (06):
[48] Well-posedness and regularity of Caputo-Hadamard fractional stochastic differential equations
Yang, Zhiwei
Zheng, Xiangcheng
Wang, Hong
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (04):
[49] FLOW INVARIANCE FOR NONLINEAR PARTIAL DIFFERENTIAL DELAY EQUATIONS
Ruess, Wolfgang M.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (08) : 4367 - 4403
[50] ON THE CONVERGENCE OF LOCALLY ONE-DIMENSIONAL SCHEMES FOR THE DIFFERENTIAL EQUATION IN PARTIAL DERIVATIVES OF FRACTIONAL ORDERS IN A MULTIDIMENSIONAL DOMAIN
Bazzaev, Alexander K.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2023, 20 (02): : 1064 - 1078

← 1 2 3 4 5 →