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On approximate controllability of non-autonomous measure driven systems with non-instantaneous impulse

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  • Kumar, Surendra

Abstract

It is known that the systems without any restriction on their Zeno behavior are immersed in an enormous type of hybrid system. This article deals with the concept of approximate controllability for a non-autonomous measure-driven system enforced by not instantaneous impulse. A bunch of new sufficient hypotheses is created to justify the solvability and approximate controllability of the system. We apply the fixed point technique and the theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. Moreover, the measured differential equations are the generalization of ordinary impulsive differential equations. Thus, our findings are more general than that found in the literature. Finally, an example is included that demonstrates the effectiveness of the developed theory.

Suggested Citation

  • Kumar, Surendra, 2023. "On approximate controllability of non-autonomous measure driven systems with non-instantaneous impulse," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007639
    DOI: 10.1016/j.amc.2022.127695
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    References listed on IDEAS

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    1. Cao, Yueju & Sun, Jitao, 2017. "Controllability of measure driven evolution systems with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 119-126.
    2. Yueju Cao & Jitao Sun, 2018. "Approximate controllability of semilinear measure driven systems," Mathematische Nachrichten, Wiley Blackwell, vol. 291(13), pages 1979-1988, September.
    3. Lina Ma & Haibo Gu & Yiru Chen & Muslim Malik, 2021. "Approximate Controllability of Neutral Measure Evolution Equations with Nonlocal Conditions," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, January.
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