Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion
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 sq...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1045760 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546852169318400 |
|---|---|
| author | Jia Mu Jiecuo Nan Yong Zhou |
| author_facet | Jia Mu Jiecuo Nan Yong Zhou |
| author_sort | Jia Mu |
| collection | DOAJ |
| description | 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-mean S-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. |
| format | Article |
| id | doaj-art-06cc760a82cb47ce8172a36abea3ebef |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-06cc760a82cb47ce8172a36abea3ebef2025-02-03T06:46:42ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/10457601045760Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian MotionJia Mu0Jiecuo Nan1Yong Zhou2Key Laboratory of Streaming Data Computing Technologies and Application, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Xiangtan University, Xiangtan, Hunan 411105, ChinaIn 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-mean S-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.http://dx.doi.org/10.1155/2020/1045760 |
| spellingShingle | Jia Mu Jiecuo Nan Yong Zhou Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion Complexity |
| title | Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion |
| title_full | Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion |
| title_fullStr | Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion |
| title_full_unstemmed | Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion |
| title_short | Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion |
| title_sort | existence and stability of square mean s asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional brownian motion |
| url | http://dx.doi.org/10.1155/2020/1045760 |
| work_keys_str_mv | AT jiamu existenceandstabilityofsquaremeansasymptoticallyperiodicsolutionstoafractionalstochasticdiffusionequationwithfractionalbrownianmotion AT jiecuonan existenceandstabilityofsquaremeansasymptoticallyperiodicsolutionstoafractionalstochasticdiffusionequationwithfractionalbrownianmotion AT yongzhou existenceandstabilityofsquaremeansasymptoticallyperiodicsolutionstoafractionalstochasticdiffusionequationwithfractionalbrownianmotion |