On the controllability of fractional functional integro-differential systems with an infinite delay in Banach spaces

In this manuscript, we study the sufficient conditions for controllability for fractional functional integro-differential systems involving the Caputo fractional derivative of order alpha is an element of(0, 1] in Banach spaces. Our main approach is based on fractional calculus, the properties of characteristic solution operators, Monch's fixed point theorem via measures of noncompactness. Particularly, these results are under some weakly compactness conditions. An example is presented in the end to show the applications of the obtained abstract results.