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Conformable Fractional Stochastic Differential Inclusions Driven by Poisson Jumps with Optimal Control and Clarke Subdifferential

Author

Listed:
  • S. Varshini

    (Sri Eshwar College of Engineering)

  • K. Ravikumar

    (PSG College of Arts & Science)

  • K. Ramkumar

    (PSG College of Arts & Science)

  • Hamdy M. Ahmed

    (El-Shorouk Academy)

Abstract

This manuscript is devoted to analysing the solvability and optimal control of a conformable fractional stochastic differential inclusion with Clarke subdifferential and deviated argument. The proposed conformable fractional impulsive inclusion system’s solvability in Hilbert space is established by employing fractional calculus, multivalued analysis, stochastic analysis, semigroup theory and a multivalued fixed point theorem. Furthermore, under some suitable assumptions, the existence of optimal control is derived by employing Balder’s theorem. Lastly, an application is provided to validate the developed theoretical results.

Suggested Citation

  • S. Varshini & K. Ravikumar & K. Ramkumar & Hamdy M. Ahmed, 2025. "Conformable Fractional Stochastic Differential Inclusions Driven by Poisson Jumps with Optimal Control and Clarke Subdifferential," Journal of Theoretical Probability, Springer, vol. 38(2), pages 1-26, June.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:2:d:10.1007_s10959-025-01414-z
    DOI: 10.1007/s10959-025-01414-z
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    References listed on IDEAS

    as
    1. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).
    2. Xiao, Guanli & Wang, JinRong & O’Regan, Donal, 2020. "Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Hamdy M. Ahmed & Reda A. Elbarkouky & Othman A. M. Omar & Maria Alessandra Ragusa, 2021. "Models for COVID-19 Daily Confirmed Cases in Different Countries," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    Full references (including those not matched with items on IDEAS)

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