Abstract
In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, ?-norm, fractional calculus, and Krasnoselskii's fixed point theorem. An example is provided to illustrate the applicability of the main results.
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