This article is mainly focusing on the approximate controllability of neutral integro-differential stochastic equations with state-dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered system. Next, we extend our study to the system with non-local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained.

中文翻译：

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状态依赖时滞的中性积分微分随机系统的近似可控性结果

本文主要研究具有状态相关时滞的中性积分微分随机方程的近似可控性。应用半群理论和求解算子的一些思想证明了本文的主要结果。首先，研究温和解的存在性，然后讨论所考虑系统的近似可控性。接下来，我们将研究扩展到具有非本地条件的系统。最后，提出了理论应用来证明所获得的可控性结果的有效性。