Abstract This manuscript is concerned with the approximate controllability problem of Hilfer fractional stochastic differential system (HFSDS) with Rosenblatt process and Poisson jumps. We derive the main results in stochastic settings by employing analytic resolvent operators, fractional calculus and fixed point theory. Further, we express the theoretical result with an example.

中文翻译：

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具有 Rosenblatt 过程和 Poisson 跳跃的非线性 Hilfer 分数随机微分系统的近似可控性

摘要 本手稿涉及具有 Rosenblatt 过程和 Poisson 跳跃的 Hilfer 分数随机微分系统 (HFSDS) 的近似可控性问题。我们通过采用解析解析算子、分数阶微积分和不动点理论在随机设置中推导出主要结果。进一步，我们用一个例子来表达理论结果。