Abstract and Applied Analysis
Volume 2013 (2013), Article ID 769257, 9 pages
http://dx.doi.org/10.1155/2013/769257
Research Article

Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

R. Sakthivel,1 P. Revathi,2 and N. I. Mahmudov3

1Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
2Department of Mathematics, Anna University of Technology, Coimbatore 641 047, India
3Department of Mathematics, Eastern Mediterranean University, Gazimagusa, Mersin 10, Turkey

Received 11 September 2012; Accepted 8 November 2012

Academic Editor: Elena Braverman

Copyright © 2013 R. Sakthivel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.