The paper investigated the exact controllability of delayed fractional evolution systems of order $\alpha \in (1,2)$ in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term $f$ is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory.