Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay
In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an alpha-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/206/abstr.html |
| _version_ | 1818188840613969920 |
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| author | Zuomao Yan Hongwu Zhang |
| author_facet | Zuomao Yan Hongwu Zhang |
| author_sort | Zuomao Yan |
| collection | DOAJ |
| description | In this article, we study the asymptotical stability in
p-th moment of mild solutions to a class of fractional impulsive
partial neutral stochastic integro-differential equations
with state-dependent delay in Hilbert spaces.
We assume that the linear part of this equation generates an
alpha-resolvent operator and transform it into an integral equation.
Sufficient conditions for the existence and asymptotic stability of
solutions are derived by means of the Krasnoselskii-Schaefer type
fixed point theorem and properties of the alpha-resolvent operator.
An illustrative example is also provided. |
| first_indexed | 2024-12-11T23:33:19Z |
| format | Article |
| id | doaj.art-ac0ae414087549d6a8112b6ce93d7f1a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T23:33:19Z |
| publishDate | 2013-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-ac0ae414087549d6a8112b6ce93d7f1a2022-12-22T00:45:57ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-09-012013206,129Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delayZuomao Yan0Hongwu Zhang1 Hexi Univ., Zhangye, Gansu, China Hexi Univ., Zhangye, Gansu, China In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an alpha-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and asymptotic stability of solutions are derived by means of the Krasnoselskii-Schaefer type fixed point theorem and properties of the alpha-resolvent operator. An illustrative example is also provided.http://ejde.math.txstate.edu/Volumes/2013/206/abstr.htmlAsymptotic stabilityimpulsive neutral integro-differential equationsstochastic integro-differential equationsalpha-resolvent operator |
| spellingShingle | Zuomao Yan Hongwu Zhang Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay Electronic Journal of Differential Equations Asymptotic stability impulsive neutral integro-differential equations stochastic integro-differential equations alpha-resolvent operator |
| title | Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay |
| title_full | Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay |
| title_fullStr | Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay |
| title_full_unstemmed | Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay |
| title_short | Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay |
| title_sort | asymptotic stability of fractional impulsive neutral stochastic partial integro differential equations with state dependent delay |
| topic | Asymptotic stability impulsive neutral integro-differential equations stochastic integro-differential equations alpha-resolvent operator |
| url | http://ejde.math.txstate.edu/Volumes/2013/206/abstr.html |
| work_keys_str_mv | AT zuomaoyan asymptoticstabilityoffractionalimpulsiveneutralstochasticpartialintegrodifferentialequationswithstatedependentdelay AT hongwuzhang asymptoticstabilityoffractionalimpulsiveneutralstochasticpartialintegrodifferentialequationswithstatedependentdelay |