A note on approximate controllability of second-order impulsive stochastic Volterra-Fredholm integrodifferential system with infinite delay

This manuscript examines the approximate controllability of a second-order stochastic Volterra-Fredholm integrodifferential system including delay and impulses. Primarily, by utilizing stochastic theory, the cosine family of operators, and the fixed point approach, we verify the existence of mild solutions for the given system. In particular, we establish a new set of sufficient requirements for the approximate controllability of the system. On the condition that the associated linear system is approximately controllable, the outcome is derived. In addition, we extend our system with nonlocal conditions. To demonstrate the theory of the primary outcomes, an example is shown.