Approximate controllability of non-instantaneous impulsive semi-linear neutral differential equations with non-local conditions and unbounded delay

In this work, we study the approximate controllability for retarded neutral differential equations with unbounded delay, non-instantaneous impulses, and non-local conditions. First, we set the problem in a natural Banach phase space satisfying Hale-Kato axiomatic Theory about the phase space for retarded ordinary equations with unbounded delay. Second, we assume some conditions on the nonlinear terms to achieve the approximate controllability using the technique developed by Bashirov and Ghahramanlou [6], which avoids the use of fixed point theorems.