Optimal and total controllability approach of non-instantaneous Hilfer fractional derivative with integral boundary condition

The focus of this work is on the absolute controllability of Hilfer impulsive non-instantaneous neutral derivative (HINND) with integral boundary condition of any order. Total controllability refers to the system’s ability to be controlled during the impulse time. Kuratowski measure and semigroup theory in Banach space yield the results. Furthermore, we talked about optimal controllability in conjunction with appropriate limitations. Our established outcomes are described using an example.