Electron. J. Diff. Equ., Vol. 2013 (2013), No. 206, pp. 1-29.

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

Zuomao Yan, Hongwu Zhang

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.

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Zuomao Yan
Department of Mathematics, Hexi University
Zhangye, Gansu 734000, China
email: yanzuomao@163.com
Hongwu Zhang
Department of Mathematics, Hexi University
Zhangye, Gansu 734000, China
email: zh-hongwu@163.com

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