IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i11p2447-d1155580.html
   My bibliography  Save this article

On Fractional-Order Discrete-Time Reaction Diffusion Systems

Author

Listed:
  • Othman Abdullah Almatroud

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

  • Amel Hioual

    (Laboratory of Dynamical Systems and Control, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria)

  • Adel Ouannas

    (Department of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria)

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy)

Abstract

Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration.

Suggested Citation

  • Othman Abdullah Almatroud & Amel Hioual & Adel Ouannas & Giuseppe Grassi, 2023. "On Fractional-Order Discrete-Time Reaction Diffusion Systems," Mathematics, MDPI, vol. 11(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2447-:d:1155580
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/11/2447/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/11/2447/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    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. Zhao, Zhong & Pang, Liuyong & Li, Qiuying, 2021. "Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    3. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

    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:gam:jmathe:v:11:y:2023:i:11:p:2447-:d:1155580. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.