Study on the controllability of Hilfer fractional differential system with and without impulsive conditions via infinite delay

In this manuscript, we investigate the controllability of two different kinds of Hilfer fractional differential equations with an almost sectorial operator and infinite delay. First, we demonstrate the exact controllability of the Hilfer fractional system using the measure of noncompactness. Next, we develop the results for the controllability of the system under impulsive conditions. Finally, to show how the key findings may be utilised, applications are presented.