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.