Controllability of the impulsive functional BBM equation with nonlinear term involving spatial derivative

For a broad class of control systems modeling real-life problems, delays and impulses are natural properties that do not modify their behavior. So, we conjecture that under certain conditions delays and abrupt changes as perturbations of a system do not modify properties such as controllability. In this regard, we prove the approximate controllability of the impulsive functional Benjamin-Bona-Mahony (BBM) equation with nonlinear term involving spatial derivative, this can be achieved using the technique avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval.