Result on Controllability of Hilfer fractional integro-differential equations of Sobolev-type with Non-instantaneous Impulses

This paper is concerned with the existence and controllability results for a class of Hilfer fractional differential equations of Sobolev-type with non-instantaneous impulse in Banach space. In order to bring off the main results, the author used the theory of propagation family {.9'(tau)}tau >= 0 (generated by the operator pair (.91, ?)), measure of non-compactness, and the fixed point methods. The primary goal of this study is to determine the controllability of a dynamical system without assuming that ?-1 is a bounded operator, and no relationship between the domain of the operators .91 and ?. At the end, we provide an example to illustrate the main results.