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<p>This study investigates the existence, uniqueness, stability and controllability of solution of first order non-linear adjoint impulsive delay dynamic system on time scale. The problem is formulated by employing the theory of time scale, allowing us to apply our results to various time domains, including continuous and discrete cases. The existence and uniqueness of solutions are established using the Banach fixed point theorem. Control functions and the Picard operator are used to handle controllability in our proposed scenarios. By applying Grönwall’s inequality on a time scale, we also verified the Hyers–Ulam stability. At the end, we validated our analytical findings with two numerical examples and simulations on different time scales.</p>

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Qualitative Results of Non-linear Adjoint Dynamic System with Delays and Impulses on Arbitrary Time Domains

  • 期刊论文

  • 发表日期：

    2024年12月31日

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  • Syed Omar Shah,
  • Vipin Kumar,
  • Sanket Tikare,
  • Rizwan Rizwan,
  • Usman Riaz

摘要

This study investigates the existence, uniqueness, stability and controllability of solution of first order non-linear adjoint impulsive delay dynamic system on time scale. The problem is formulated by employing the theory of time scale, allowing us to apply our results to various time domains, including continuous and discrete cases. The existence and uniqueness of solutions are established using the Banach fixed point theorem. Control functions and the Picard operator are used to handle controllability in our proposed scenarios. By applying Grönwall’s inequality on a time scale, we also verified the Hyers–Ulam stability. At the end, we validated our analytical findings with two numerical examples and simulations on different time scales.