Approximate Controllability of Non‐Autonomous Differential Systems Having Instantaneous and Non‐Instantaneous Impulses

This article evaluates a novel class of non‐autonomous differential systems involving instantaneous and non‐instantaneous impulses in Hilbert spaces. Initially, we investigate the presence of a mild solution for the aforementioned system under some simple conditions on the system parameters. Next, we constructed a new set of sufficient hypotheses for investigating the approximate controllability of the nonlinear system. The evolution operator and fixed point method are frequently employed to justify the existence of a solution. At the end, an example is given to illustrate and validate the proposed theory.