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Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

Author

Listed:
  • Ghada AlNemer

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mohamed Hosny

    (Department of Electrical Engineering, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt)

  • Ramalingam Udhayakumar

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India)

  • Ahmed M. Elshenhab

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided.

Suggested Citation

  • Ghada AlNemer & Mohamed Hosny & Ramalingam Udhayakumar & Ahmed M. Elshenhab, 2024. "Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process," Mathematics, MDPI, vol. 12(11), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1729-:d:1407283
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    References listed on IDEAS

    as
    1. Hamdy M. Ahmed, 2015. "Semilinear Neutral Fractional Stochastic Integro-Differential Equations with Nonlocal Conditions," Journal of Theoretical Probability, Springer, vol. 28(2), pages 667-680, June.
    2. Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    3. Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
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