This paper dealt with the infinite controllability of delayed evolution inclusions with $\alpha$-order fractional derivatives in Fr $\acute{e}$chet spaces, where $\alpha \in (1,2)$. The controllability conclusion was acquired without any compactness for the nonlinear term, the cosine family, and the sine family. The investigation was based on a nonlinear alternative and the cosine family theory. An application of our findings was provided.