The problem of approximate controllability is investigated in this paper for a class of fractional stochastic differential equations driven by fractional Brownian motion with non-instantaneous impulses and Poisson jumps. The results are obtained by employing the η-resolvent family and Krasnoselskii's fixed point theorem. Further, we derive the trajectory controllability for the proposed stochastic control system. Finally, an example is provided to illustrate the obtained theory.

中文翻译：

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具有非瞬时脉冲和泊松跳跃的分数阶随机微分方程的近似和轨迹可控性

本文研究了一类由具有非瞬时脉冲和泊松跳跃的分数布朗运动驱动的分数随机微分方程的近似可控性问题。结果是通过使用η -resolvent 族和 Krasnoselskii 不动点定理获得的。此外，我们推导出了所提出的随机控制系统的轨迹可控性。最后，提供了一个例子来说明所得到的理论。