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

Author

Listed:
  • Ravikumar Kasinathan

    (PSG College of Arts & Science)

  • Varshini Sandrasekaran

    (PSG College of Arts & Science)

  • Ramkumar Kasinathan

    (PSG College of Arts & Science)

  • Rajesh Dhayal

    (Thapar Institute of Engineering and Technology)

Abstract

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.

Suggested Citation

  • Ravikumar Kasinathan & Varshini Sandrasekaran & Ramkumar Kasinathan & Rajesh Dhayal, 2025. "Non-Instantaneous Impulsive Fractional Stochastic Differential Systems with Damping: Optimal Controls and Trajectory Controllability," Journal of Theoretical Probability, Springer, vol. 38(3), pages 1-27, September.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01423-y
    DOI: 10.1007/s10959-025-01423-y
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    References listed on IDEAS

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    1. Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    2. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
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