Approximate Controllability for a Class of Instantaneous and Non-instantaneous Impulsive Semilinear Systems

摘要

In this manuscript, the approximate controllability is encountered for a system involving instantaneous and non-instantaneous impulses. The theory of semigroup and Sadovskii’s fixed point theorem are used to prove our main results. In the direction of controllability for a functional differential equations, a problem consists of either instant impulses or non-instant impulses separately. This is the reason that makes the study of the considered problem more interesting. We also make an observation related to high blood sugar level that is quite natural to relate with our problem. In the end, an example is given to validate the developed theory.