Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays
We study the existence and asymptotic stability in pth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point tec...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/769257 |
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| author | R. Sakthivel P. Revathi N. I. Mahmudov |
| author_facet | R. Sakthivel P. Revathi N. I. Mahmudov |
| author_sort | R. Sakthivel |
| collection | DOAJ |
| description | We study the existence and asymptotic stability in pth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite
delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory. |
| format | Article |
| id | doaj-art-50640ba4fce94e869c41542efbb83e0b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-50640ba4fce94e869c41542efbb83e0b2025-02-03T01:30:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/769257769257Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite DelaysR. Sakthivel0P. Revathi1N. I. Mahmudov2Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of KoreaDepartment of Mathematics, Anna University of Technology, Coimbatore 641 047, IndiaDepartment of Mathematics, Eastern Mediterranean University, Gazimagusa, Mersin 10, TurkeyWe study the existence and asymptotic stability in pth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory.http://dx.doi.org/10.1155/2013/769257 |
| spellingShingle | R. Sakthivel P. Revathi N. I. Mahmudov Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays Abstract and Applied Analysis |
| title | Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays |
| title_full | Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays |
| title_fullStr | Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays |
| title_full_unstemmed | Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays |
| title_short | Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays |
| title_sort | asymptotic stability of fractional stochastic neutral differential equations with infinite delays |
| url | http://dx.doi.org/10.1155/2013/769257 |
| work_keys_str_mv | AT rsakthivel asymptoticstabilityoffractionalstochasticneutraldifferentialequationswithinfinitedelays AT prevathi asymptoticstabilityoffractionalstochasticneutraldifferentialequationswithinfinitedelays AT nimahmudov asymptoticstabilityoffractionalstochasticneutraldifferentialequationswithinfinitedelays |