MAXIMUM PRINCIPLES FOR A CLASS OF GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATIONS

被引：6

作者：

Zeng, Shengda ^{[1
,3
]}

Migorski, Stanislaw ^{[2
,3
]}

Van Thien Nguyen ^{[4
]}

Bai, Yunru ^{[3
]}

机构：

[1] Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Peoples R China

[2] Chengdu Univ Informat Technol, Coll Appl Math, Chengdu 610225, Sichuan, Peoples R China

[3] Jagiellonian Univ Krakow, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

[4] FPT Univ, Dept Math, Educ Zone, Thach Ward, Hoa Lac High Tech Pk,Km29 Thang Long Highway, Hanoi, Vietnam

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 03期

基金：

欧盟地平线“2020”;

关键词：

maximum principles; extremum principles; variable-order fractional calculus; time-space fractional diffusion equation; Riesz-Caputo fractional derivative;

D O I：

10.1515/fca-2020-0041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two significant inequalities for generalized time fractional derivatives at extreme points are obtained. Then, we apply the inequalities to establish the maximum principles for multi-term time-space fractional variable-order operators. Finally, we employ the principles to investigate two kinds of diffusion equations involving generalized time-fractional Caputo derivatives and space-fractional Riesz-Caputo derivatives.

引用

页码：822 / 836

页数：15

共 50 条

[41] A maximum principle for solutions of a class of quasilinear elliptic equations on unbounded domains
Jin, ZR
Lancaster, K
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (7-8) : 1271 - 1281
[42] Maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction
Monticelli, Dario D.
Payne, Kevin R.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (07) : 1993 - 2026
[43] MAXIMUM AND MINIMUM PRINCIPLES FOR NONLINEAR TRANSPORT EQUATIONS ON DISCRETE-SPACE DOMAINS
Volek, Jonas
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
[44] ON GRADIENT MAXIMUM-PRINCIPLES FOR QUASI-LINEAR ELLIPTIC-EQUATIONS
PAYNE, LE
PHILIPPIN, GA
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (03) : 387 - 398
[45] Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
Monticelli, Dario Daniele
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (03) : 611 - 654
[46] On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method
Mudunuru, M. K.
Nakshatrala, K. B.
JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 305 : 448 - 493
[47] Regularity results for a class of generalized surface quasi-geostrophic equations
Lazar, Omar
Xue, Liutang
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 130 : 200 - 250
[48] Maximum principles and nonexistence results for radial solutions to equations involving p-Laplacian
Adamowicz, Tomasz
Katamajska, Agnieszka
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (13) : 1618 - 1627
[49] Finite difference scheme for time-space fractional diffusion equation with fractional boundary conditions
Xie, Changping
Fang, Shaomei
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3473 - 3487
[50] A numerical approach for solving a class of variable-order fractional functional integral equations
Keshi, Farzad Khane
Moghaddam, Behrouz Parsa
Aghili, Arman
COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) : 4821 - 4834

← 1 2 3 4 5 →