This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro‐differential equation with infinite delay. We study our primary outcomes by utilizing the theoretical concepts related to the fractional calculus and Krasnoselskii's fixed point theorem. First, we prove the approximate controllability of the fractional evolution system. Then, we extend our results to the concept of nonlocal conditions. Last, we provide a theoretical application to assist in the effectiveness of the discussion.

中文翻译：

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关于希尔弗分数中性随机时滞积分-微分系统的近似可控性的新结果

该手稿主要关注具有无限延迟的Hilfer分数阶中立随机积分微分方程的近似可控性。我们通过利用与分数演算和Krasnoselskii不动点定理有关的理论概念来研究主要结果。首先，我们证明了分数演化系统的近似可控性。然后，我们将结果扩展到非本地条件的概念。最后，我们提供了理论上的应用来协助讨论的有效性。