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Existence and uniqueness of solutions for stochastic differential equations of fractional-order \(q > 1\) with finite delays. (English) Zbl 1422.34083

Summary: This paper is concerned with stochastic differential equations of fractional-order \(q \in(m-1, m)\) (where \(m \in \mathbb{Z}\) and \(m \geq 2\)) with finite delay at a space \(BC ([ - \tau, 0]; R^{d})\). Some sufficient conditions are obtained for the existence and uniqueness of solutions for these stochastic fractional differential systems by applying the Picard iterations method and the generalized Gronwall inequality.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34K50 Stochastic functional-differential equations
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