Yan, Zuomao; Zhang, Hongwu Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay. (English) Zbl 1293.34102 Electron. J. Differ. Equ. 2013, Paper No. 206, 29 p. (2013). Summary: 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. Cited in 25 Documents MSC: 34K37 Functional-differential equations with fractional derivatives 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations 34K30 Functional-differential equations in abstract spaces 34K50 Stochastic functional-differential equations 47N20 Applications of operator theory to differential and integral equations 34K45 Functional-differential equations with impulses 34K20 Stability theory of functional-differential equations 34K40 Neutral functional-differential equations 45K05 Integro-partial differential equations Keywords:asymptotic stability; impulsive neutral integro-differential equations; stochastic integro-differential equations; alpha-resolvent operator PDFBibTeX XMLCite \textit{Z. Yan} and \textit{H. Zhang}, Electron. J. Differ. Equ. 2013, Paper No. 206, 29 p. (2013; Zbl 1293.34102) Full Text: EMIS