On neutral impulsive stochastic integro-differential equations with infinite delays via fractional operators

Authors:
Aihong Lin;Yong Ren;Ningmao Xia
Affiliations:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;Department of Mathematics, Anhui Normal University, Wuhu 241000, China;Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

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Abstract

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.