Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion

被引：1

作者：

Mu, Jia ^{[1
,2
]}

Nan, Jiecuo ^{[2
]}

Zhou, Yong ^{[3
,4
]}

机构：

[1] Northwest Minzu Univ, Key Lab Streaming Data Comp Technol & Applicat, Lanzhou 730000, Peoples R China

[2] Northwest Minzu Univ, Sch Math & Comp Sci, Lanzhou 730000, Peoples R China

[3] Xiangtan Univ, Sch Math & Comp Sci, Xiangtan 411105, Hunan, Peoples R China

[4] King Abdulaziz Univ, Nonlinear Anal & Appl Math Res Grp, Fac Sci, Jeddah 21589, Saudi Arabia

来源：

COMPLEXITY | 2020年 / 2020卷

基金：

中国国家自然科学基金;

关键词：

EVOLUTION-EQUATIONS; EXPONENTIAL STABILITY; MOMENT STABILITY; HURST PARAMETER; DRIVEN; BEHAVIOR; SYSTEMS; REGULARITY; CALCULUS; DELAY;

D O I：

10.1155/2020/1045760

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a generalized Gronwall inequality is demonstrated, playing an important role in the study of fractional differential equations. In addition, with the fixed-point theorem and the properties of Mittag-Leffler functions, some results of the existence as well as asymptotic stability of square-meanS-asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. In the end, an example of numerical simulation is given to illustrate the effectiveness of our theory results.

引用

页数：15

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