This paper addresses some interesting results of mild solutions to fractional evolution systems with order $ \alpha\in (1,2) $ in Banach spaces as well as the controllability problem. Firstly, we deduce a new representation of solution operators and give a new concept of mild solutions for the objective equations by the Laplace transform and Mainardi's Wright-type function, and then we proceed to establish a new compact result of the solution operators when the sine family is compact. Secondly, the controllability results of mild solutions are obtained. Finally, an example is presented to illustrate the main results.

中文翻译：

---

有阶分数演化系统可控性的新结果 \begin{document}$ \alpha\in (1,2) $\end{document}

本文讨论了 Banach 空间中阶数为 $\alpha\in (1,2) $ 的分数演化系统的温和解以及可控性问题的一些有趣结果。首先，我们通过拉普拉斯变换和 Mainardi 的 Wright 型函数推导了解算子的新表示，并给出了目标方程的温和解的新概念，然后我们着手建立了当正弦时解算子的新紧致结果。家庭紧凑。其次，得到了温和解的可控性结果。最后，给出一个例子来说明主要结果。