Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 206, pp. 1-29.

Title: Asymptotic stability of fractional  impulsive  neutral  stochastic
       partial integro-differential equations with state-dependent delay

Authors: Zuomao Yan   (Hexi Univ., Zhangye, Gansu, China)
         Hongwu Zhang (Hexi Univ., Zhangye, Gansu, China)

Abstract:
 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.

Submitted April 28, 2013. Published September 18, 2013.
Math Subject Classifications: 34A37, 60H15, 35R60, 93E15, 26A33.
Key Words: Asymptotic stability; impulsive  neutral integro-differential equations;
           stochastic  integro-differential equations; alpha-resolvent operator.