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<p>We investigate a new class of impulsive fractional stochastic differential systems with damping effects in Banach spaces, where the abrupt changes occur suddenly at specific points and extend over finite time intervals. Initially, we explore the solvability of the system by applying stochastic analysis, fractional calculus, and the Banach contraction principle. Next, we utilize Balder’s theorem to establish the existence of optimal controls. Additionally, under certain conditions, we establish the trajectory controllability of the system by employing generalized Grönwall’s inequality. An example is provided to demonstrate the validity of the results.</p>

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Non-Instantaneous Impulsive Fractional Stochastic Differential Systems with Damping: Optimal Controls and Trajectory Controllability

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Ravikumar Kasinathan,
  • Varshini Sandrasekaran,
  • Ramkumar Kasinathan,
  • Rajesh Dhayal

摘要

We investigate a new class of impulsive fractional stochastic differential systems with damping effects in Banach spaces, where the abrupt changes occur suddenly at specific points and extend over finite time intervals. Initially, we explore the solvability of the system by applying stochastic analysis, fractional calculus, and the Banach contraction principle. Next, we utilize Balder’s theorem to establish the existence of optimal controls. Additionally, under certain conditions, we establish the trajectory controllability of the system by employing generalized Grönwall’s inequality. An example is provided to demonstrate the validity of the results.