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Existence of solutions for nonlinear fractional stochastic differential equations. (English) Zbl 1261.34063
Summary: This paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces. Using fractional calculations, the fixed point technique, stochastic analysis and methods adopted directly from deterministic fractional equations, new set of sufficient conditions are formulated and proved for the existence of mild solutions for fractional impulsive stochastic differential equations with infinite delay. Further, we study the existence of solutions for fractional stochastic semilinear differential equations under nonlocal conditions. Examples are provided to illustrate the obtained theory.
MSC:
34K37Functional-differential equations with fractional derivatives
34K30Functional-differential equations in abstract spaces
34K45Functional-differential equations with impulses
34K50Stochastic functional-differential equations