IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2025y2025i1n2512843.html

Modeling and Stability Analysis of Time‐Dependent Free‐Fall Motion in Random Environments

Author

Listed:
  • Alireza Hatami
  • Safoura Rezaei Aderyani
  • Reza Saadati
  • Mohammad Bagher Ghaemi

Abstract

This paper examines the stability of a fractional‐order model that describes the free‐fall motion of a football in changing environmental conditions. Traditional models often overlook memory effects and nonlocal influences like air resistance, humidity, and turbulence. To tackle this issue, we enhance the classical Newtonian model by using the Hilfer fractional derivative, which includes memory and hereditary properties. We analyze the resulting equation for Ulam–Hyers–Rassias stability within the context of random Banach spaces, using distribution‐valued norms and t–norms to manage uncertainty and oscillatory behavior. We apply fixed‐point theory to establish sufficient conditions for stability and uniqueness of solutions. Numerical simulations and error analyses with special functions show the effectiveness and reliability of the proposed model, demonstrating better accuracy and stability compared to traditional methods.

Suggested Citation

  • Alireza Hatami & Safoura Rezaei Aderyani & Reza Saadati & Mohammad Bagher Ghaemi, 2025. "Modeling and Stability Analysis of Time‐Dependent Free‐Fall Motion in Random Environments," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:2512843
    DOI: 10.1155/ddns/2512843
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ddns/2512843
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ddns/2512843?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yeol Je Cho & Themistocles M. Rassias & Reza Saadati, 2013. "Stability of Function Equations in Non-Archimedean Random Spaces," Springer Optimization and Its Applications, in: Stability of Functional Equations in Random Normed Spaces, edition 127, chapter 0, pages 125-151, Springer.
    2. Yeol Je Cho & Themistocles M. Rassias & Reza Saadati, 2013. "Stability of Functional Equations in Random Normed Spaces," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-8477-6, January.
    3. Radko Mesiar & Reza Saadati, 2021. "Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
    4. Masoumeh Madadi & Reza Saadati & Manuel De la Sen, 2020. "Stability of Unbounded Differential Equations in Menger k -Normed Spaces: A Fixed Point Technique," Mathematics, MDPI, vol. 8(3), pages 1-10, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammad Maleki V. & S. Mansour Vaezpour & Reza Saadati, 2018. "Nonlinear Stability of ρ -Functional Equations in Latticetic Random Banach Lattice Spaces," Mathematics, MDPI, vol. 6(2), pages 1-12, February.
    2. Anca Croitoru & Radko Mesiar & Anna Rita Sambucini & Bianca Satco, 2022. "Special Issue on Set Valued Analysis 2021," Mathematics, MDPI, vol. 10(15), pages 1-2, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnddns:v:2025:y:2025:i:1:n:2512843. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.