Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense domain

Abstract

The controllability of a class of nondensely defined fractional dynamic delay inclusions containing Hilfer fractional derivative, nonlocal conditions, and non-instantaneous impulses in abstract spaces is investigated without compactness assumption. The existence of an integral solution and the controllability for the given problem are established relying on a condensing fixed point theorem of multivalued maps. In support, an example is given to clarify the obtained theoretical outcomes