On the Approximate Controllability of Second-Order Hilfer Fractional Integro-Differential Equations via Measure of Non-compactness

This manuscript investigates the approximate controllability results for a class of second-order Hilfer fractional integro-differential equations (HFIDEs). A new set of appropriate mild solutions has been derived. Further, the existence of mild solutions for the proposed system has been verified using Mönch fixed point theorem (MFPT) and derived sufficient condition utilizing the measure of non-compactness (MNC). The approximate controllability results of the proposed system have been established by presuming that the associated linear system is an approximate control system. Finally, for the understanding, a numerical example is included.