New results on controllability of fractional evolution systems with order $ \alpha\in (1,2) $

Abstract

<p style='text-indent:20px;'>This paper addresses some interesting results of mild solutions to fractional evolution systems with order <inline-formula><tex-math id="M2">\begin{document}$ \alpha\in (1,2) $\end{document}</tex-math></inline-formula> 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.