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Proportional Itô–Doob Stochastic Fractional Order Systems

Author

Listed:
  • Abdellatif Ben Makhlouf

    (Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia)

  • Lassaad Mchiri

    (ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, France)

  • Hakeem A. Othman

    (Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi Arabia)

  • Hafedh M. S. Rguigui

    (Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi Arabia)

  • Salah Boulaaras

    (Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Almelida 51452, Saudi Arabia)

Abstract

In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.

Suggested Citation

  • Abdellatif Ben Makhlouf & Lassaad Mchiri & Hakeem A. Othman & Hafedh M. S. Rguigui & Salah Boulaaras, 2023. "Proportional Itô–Doob Stochastic Fractional Order Systems," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2049-:d:1133215
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    References listed on IDEAS

    as
    1. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Ulam–Hyers stability of Caputo type fractional stochastic neutral differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).
    2. Abdellatif Ben Makhlouf & El-Sayed El-Hady & Salah Boulaaras & Mohamed Ali Hammami & Sundarapandian Vaidyanathan, 2022. "Stability Analysis for Differential Equations of the General Conformable Type," Complexity, Hindawi, vol. 2022, pages 1-6, April.
    3. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Certain Hadamard Proportional Fractional Integral Inequalities," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    4. Abouagwa, Mahmoud & Liu, Jicheng & Li, Ji, 2018. "Carathéodory approximations and stability of solutions to non-Lipschitz stochastic fractional differential equations of Itô-Doob type," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 143-153.
    5. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    6. Pedjeu, Jean-C. & Ladde, Gangaram S., 2012. "Stochastic fractional differential equations: Modeling, method and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 279-293.
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