Abstract
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.
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Acknowledgements
We are grateful to the anonymous reviewer and editor. Their valuable suggestions and comments helped us to improve the quality of this manuscript.
Funding
The second author is supported by the Council of Scientific & Industrial Research (CSIR), India (Grant No.: 18/12/2016(ii)EU-V).
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Surendra Kumar and Syed Mohammad Abdal declare that they have no conflict of interest.
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Kumar, S., Abdal, S.M. Approximate Controllability for a Class of Instantaneous and Non-instantaneous Impulsive Semilinear Systems. J Dyn Control Syst 28, 725–737 (2022). https://doi.org/10.1007/s10883-021-09540-7
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DOI: https://doi.org/10.1007/s10883-021-09540-7