A result on approximate controllability results for fractional neutral integro-differential equations with nonlocal and finite delay conditions in Hilbert spaces

Abstract

On the account of semigroup theory, fractional calculus, the strategy of fractional powers of operators, $\al$-norm and Krasnoselskii's fixed point theorem, this manuscript explores  some necessary conditions to establish the approximate controllability results of  fractional integro-differential systems with  nonlocal and finite delay conditions regarded in a  Hilbert space.