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On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators. (English) Zbl 1190.60045

Summary: We study the existence of mild solutions for a class of neutral impulsive stochastic integro-differential equations with infinite delays. We assume that the undelayed part generates an analytic resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the Sadovskii fixed point theorem combined with theories of analytic resolvent operators. An example is given to illustrate the theory.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
45R05 Random integral equations
60H20 Stochastic integral equations
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