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Analysis of Neutral Implicit Stochastic Hilfer Fractional Differential Equation Involving Lévy Noise with Retarded and Advanced Arguments

Author

Listed:
  • Hamza Khalil

    (Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan)

  • Akbar Zada

    (Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan)

  • Mohamed Rhaima

    (Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia)

  • Ioan-Lucian Popa

    (Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
    Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania)

Abstract

This paper investigates the qualitative properties of the solutions for neutral implicit stochastic Hilfer fractional differential equations involving Lévy noise with retarded and advanced arguments. The existence property of the solution of the aforementioned equation is demonstrated by the Mónch condition, and the uniqueness is demonstrated by the remarkable fixed point of Banach. In addition, we examine the Hyers–Ulam ( HU ) stability of the presented mathematical models. To substantiate our theoretical conclusions, a real-world example is included to illustrate their practical application.

Suggested Citation

  • Hamza Khalil & Akbar Zada & Mohamed Rhaima & Ioan-Lucian Popa, 2024. "Analysis of Neutral Implicit Stochastic Hilfer Fractional Differential Equation Involving Lévy Noise with Retarded and Advanced Arguments," Mathematics, MDPI, vol. 12(21), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3406-:d:1511153
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    References listed on IDEAS

    as
    1. Manzoor Ahmad & Akbar Zada & Jihad Ahmad & Mohamed A. Abd El Salam & Ali Ahmadian, 2022. "Analysis of Stochastic Weighted Impulsive Neutral ψ-Hilfer Integro-Fractional Differential System with Delay," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-23, March.
    2. Kui Liu & Michal Fečkan & D. O’Regan & JinRong Wang, 2019. "Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    3. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    4. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
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