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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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.495-503-1048
Main Authors: Sakthivel, R., Revathi, P., Mahmudov, N. I.
Format: Article
Language:English
Subjects:
Asymptotic properties
Brownian motion
Delay
Differential equations
Economic models
Fixed point theory
Group theory
Hilbert space
Mathematical research
Mathematics
Nonlinearity
Partial differential equations
Random variables
Stability
Stochastic differential equations
Stochasticity
Studies
Theory
Uniqueness
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/769257