In this paper, we deal with the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities of order $r\in (1,2)$. Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, and fixed point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study.

在本文中，我们处理了 Sobolev 型分数随机进化半变分阶不等式的近似可控性$r\in (1,2)$. 首先，通过使用随机分析、分数阶微积分、正余弦族算子以及多值映射的不动点定理，我们证明了分数随机演化系统的温和解的存在性。然后我们提供了一个充分条件来保证随机演化系统的近似可控性。接下来，我们的结果涵盖了涉及非局部条件的问题。最后，我们提出了理论和实际应用来支持研究的有效性。