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Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay. (English) Zbl 1293.34102
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.

##### 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
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