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Exploring Climate-Induced Oxygen–Plankton Dynamics Through Proportional–Caputo Fractional Modeling

Author

Listed:
  • Mohamed A. Barakat

    (Department of Computer Science, College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt)

  • Areej A. Almoneef

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Abd-Allah Hyder

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia)

  • Tarek Aboelenen

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

Abstract

In this work, we develop and analyze a novel fractional-order framework to investigate the interactions among oxygen, phytoplankton, and zooplankton under changing climatic conditions. Unlike standard integer-order formulations, our model incorporates a Proportional–Caputo ( PC ) fractional derivative, allowing the system dynamics to capture non-local influences and memory effects over time. Initially, we rigorously verify that a unique solution exists by suitable fixed-point theorems, demonstrating that the proposed fractional system is both well-defined and robust. We then derive stability criteria to ensure Ulam–Hyers stability (UHS), confirming that small perturbations in initial states lead to bounded variations in long-term behavior. Additionally, we explore extended UHS to assess sensitivity against time-varying parameters. Numerical simulations illustrate the role of fractional-order parameters in shaping oxygen availability and plankton populations, highlighting critical shifts in system trajectories as the order of differentiation approaches unity.

Suggested Citation

  • Mohamed A. Barakat & Areej A. Almoneef & Abd-Allah Hyder & Tarek Aboelenen, 2025. "Exploring Climate-Induced Oxygen–Plankton Dynamics Through Proportional–Caputo Fractional Modeling," Mathematics, MDPI, vol. 13(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:980-:d:1613704
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