Abstract:
In light of ideas for semigroups, fractional calculus and Banach contraction principle, this manuscript is mainly concerned with existence and controllability of fractional neutral integro-differential structures with state-dependent delay in Banach spaces. To obtain our results, our working hypotheses are that the functions determining the equation satisfy certain Lipschitz conditions of local type which is similar to the hypotheses [5]. Examples are presented to demonstrate the application of the results established.