Abstract
In this paper, we introduce a new concept called $$\alpha $$ -order cosine-resolvent family, by using the theory of fractional calculus, the concepts of measure of noncompactness and Hybrid fixed point theorem, we consider the existence of PC-mild solutions for a class of impulsive fractional hybrid evolution equation in a Banach space . Furthermore, we obtain some sufficient conditions for approximate controllability of our concern problem. At the end, an example is given to illustrate the feasibility of our results.
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