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**Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion.**
*(English)*
Zbl 1370.34137

Stochastic differential equations have many applications in science and engineering, and have been receiving much attention over the last decades. In this paper, the authors establish sufficient conditions ensuring existence and continuous dependence of mild solutions to first order stochastic impulsive differential equation with delays in a real separable Hilbert space. The approach is based on Banach’s fixed point theorem and Krasnoselski-Schaefer type fixed point theorem.

Reviewer: Xiaohu Wang (Chengdu)

### MSC:

34K50 | Stochastic functional-differential equations |

34K45 | Functional-differential equations with impulses |

34K30 | Functional-differential equations in abstract spaces |

60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |

60H20 | Stochastic integral equations |

### Keywords:

fractional Brownian motion; fixed point; mild solutions; stochastic functional differential equation
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\textit{A. Boudaoui} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 7, 2521--2541 (2017; Zbl 1370.34137)

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