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Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative

Author

Listed:
  • Abdelhamid Mohammed Djaouti

    (Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia)

  • Zareen A. Khan

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
    These authors contributed equally to this work.)

  • Muhammad Imran Liaqat

    (Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan
    These authors contributed equally to this work.)

  • Ashraf Al-Quran

    (Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in L p space by using Jensen’s, Grönwall–Bellman’s, Hölder’s, and Burkholder–Davis–Gundy’s inequalities, and the interval translation technique for a class of fractional neutral stochastic differential equations. We establish the results within the framework of the Ψ -Caputo derivative. We generalize the two situations of p = 2 and the Caputo derivative with the findings that we obtain. To help with the understanding of the theoretical results, we provide two applied examples at the end.

Suggested Citation

  • Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1037-:d:1367456
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    References listed on IDEAS

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    1. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Lili Gao & Litan Yan, 2018. "On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, November.
    3. Aziz Khan & Muhammad Imran Liaqat & Manar A. Alqudah & Thabet Abdeljawad, 2023. "Analysis Of The Conformable Temporal-Fractional Swift–Hohenberg Equation Using A Novel Computational Technique," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-17.
    4. Mao, Wei & Zhu, Quanxin & Mao, Xuerong, 2015. "Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 252-265.
    5. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    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.
    7. Xue Wang & Danfeng Luo & Zhiguo Luo & Akbar Zada, 2021. "Ulam–Hyers Stability of Caputo-Type Fractional Stochastic Differential Equations with Time Delays," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-24, March.
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