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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.
60H10Stochastic ordinary differential equations
34K50Stochastic functional-differential equations
45R05Random integral equations
60H20Stochastic integral equations
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