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

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.

Keywords

• Asymptotic stability
• impulsive neutral integro-differential equations
• stochastic integro-differential equations
• alpha-resolvent operator