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.

中文翻译：

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一类瞬时和非瞬时脉冲半线性系统的近似可控性

在此手稿中，遇到涉及瞬时和非瞬时脉冲的系统会遇到近似的可控制性。半群理论和萨多夫斯基定点定理被用来证明我们的主要结果。在泛函微分方程的可控制性方向上，问题是分别由瞬时脉冲或非瞬时脉冲组成。这就是使对所考虑问题的研究更加有趣的原因。我们还进行了与高血糖水平相关的观察，这很自然地与我们的问题有关。最后，给出一个例子来验证所发展的理论。