## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 769257, 9 pages.

### Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

R. Sakthivel, P. Revathi, and N. I. Mahmudov

#### Abstract

We study the existence and asymptotic stability in *p*th 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.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013 (2013), Article ID 769257, 9 pages.

**Dates**

First available in Project Euclid: 18 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1366306764

**Digital Object Identifier**

doi:10.1155/2013/769257

**Mathematical Reviews number (MathSciNet)**

MR3035189

**Zentralblatt MATH identifier**

1269.60059

#### Citation

Sakthivel, R.; Revathi, P.; Mahmudov, N. I. Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays. Abstr. Appl. Anal. 2013 (2013), Article ID 769257, 9 pages. doi:10.1155/2013/769257. https://projecteuclid.org/euclid.aaa/1366306764