Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion
Abstract The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016)...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1411-z |
| _version_ | 1818381318786908160 |
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| author | Pengju Duan Yong Ren |
| author_facet | Pengju Duan Yong Ren |
| author_sort | Pengju Duan |
| collection | DOAJ |
| description | Abstract The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions. |
| first_indexed | 2024-12-14T02:32:41Z |
| format | Article |
| id | doaj.art-193f18b0e8944b8eb48c2bef4ff735a6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T02:32:41Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-193f18b0e8944b8eb48c2bef4ff735a62022-12-21T23:20:12ZengSpringerOpenAdvances in Difference Equations1687-18472017-11-012017111510.1186/s13662-017-1411-zAttracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motionPengju Duan0Yong Ren1School of Mathematics and Statistics, Suzhou UniversityDepartment of Mathematics, Anhui Normal UniversityAbstract The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions.http://link.springer.com/article/10.1186/s13662-017-1411-zimpulsive integral inequalityfractional Brownian motionattracting setquasi-invariant setstochastic integro-differential equation |
| spellingShingle | Pengju Duan Yong Ren Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion Advances in Difference Equations impulsive integral inequality fractional Brownian motion attracting set quasi-invariant set stochastic integro-differential equation |
| title | Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion |
| title_full | Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion |
| title_fullStr | Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion |
| title_full_unstemmed | Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion |
| title_short | Attracting and quasi-invariant sets of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion |
| title_sort | attracting and quasi invariant sets of neutral stochastic integro differential equations with impulses driven by fractional brownian motion |
| topic | impulsive integral inequality fractional Brownian motion attracting set quasi-invariant set stochastic integro-differential equation |
| url | http://link.springer.com/article/10.1186/s13662-017-1411-z |
| work_keys_str_mv | AT pengjuduan attractingandquasiinvariantsetsofneutralstochasticintegrodifferentialequationswithimpulsesdrivenbyfractionalbrownianmotion AT yongren attractingandquasiinvariantsetsofneutralstochasticintegrodifferentialequationswithimpulsesdrivenbyfractionalbrownianmotion |