Controllability of switched Hilfer neutral fractional dynamic systems with impulses

The aim of this work is to investigate the controllability of a class of switched Hilfer neutral fractional systems with non-instantaneous impulses in the finite-dimensional spaces. We construct a new class of control function that controls the system at the final time of the time-interval and controls the system at each of the impulsive points i.e. we give the so-called total controllability results. Also, we extend these results to the corresponding integro-system. We mainly use the fixed point theorem, Laplace transformation, Mittag-Leffler function, Gramian type matrices and fractional calculus to establish these results. In the end, we provide a simulated example to verify the obtained analytical results.