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A Novel Fixed-Point Iterative Process for Multivalued Mappings Applied in Solving a HIV Model of Fractional Order

Author

Listed:
  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh P.O. Box 90950, Saudi Arabia)

  • Godwin Amechi Okeke

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri P.M.B. 1526, Imo State, Nigeria)

  • Cyril Ifeanyichukwu Ugwuogor

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri P.M.B. 1526, Imo State, Nigeria)

Abstract

We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of numerical illustrations and examples was constructed to validate our results. As an application, we propose a novel method for solving a certain fractional differential equation using our newly developed iterative scheme. Our results extend, unify, and improve several of the known results in the literature.

Suggested Citation

  • Rubayyi T. Alqahtani & Godwin Amechi Okeke & Cyril Ifeanyichukwu Ugwuogor, 2025. "A Novel Fixed-Point Iterative Process for Multivalued Mappings Applied in Solving a HIV Model of Fractional Order," Mathematics, MDPI, vol. 13(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:739-:d:1598771
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    References listed on IDEAS

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    1. Ahmed Kajouni & Ahmed Chafiki & Khalid Hilal & Mohamed Oukessou, 2021. "A New Conformable Fractional Derivative and Applications," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-5, November.
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