IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2023y2023i1n6646284.html

Green’s Functions on Various Time Scales for the Time‐Fractional Reaction‐Diffusion Equation

Author

Listed:
  • Alexey Zhokh
  • Peter Strizhak

Abstract

The time‐fractional diffusion equation coupled with a first‐order irreversible reaction is investigated by employing integral transforms. We derive Green’s functions for short and long times via approximations of the Mittag‐Leffler function. The time value for which the crossover between short‐ and long‐time asymptotic holds is presented in explicit form. Based on the developed Green’s functions, the exact analytic asymptotic solutions of the time‐fractional reaction‐diffusion equation are obtained. The applicability of the obtained solutions is demonstrated via quantification of the reaction‐diffusion kinetics during heterogeneous catalytic chitin conversion to chitosan.

Suggested Citation

  • Alexey Zhokh & Peter Strizhak, 2023. "Green’s Functions on Various Time Scales for the Time‐Fractional Reaction‐Diffusion Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:6646284
    DOI: 10.1155/2023/6646284
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/6646284
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/6646284?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. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    3. Hari M. Srivastava & Khaled Mohammed Saad & Walid M. Hamanah, 2022. "Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations," Mathematics, MDPI, vol. 10(7), pages 1-13, 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. P. Chellamani & K. Julietraja & Ammar Alsinai & Hanan Ahmed, 2022. "A Fuzzy Fractional Order Approach to SIDARTHE Epidemic Model for COVID‐19," Complexity, John Wiley & Sons, vol. 2022(1).
    2. Li, Peiluan & Gao, Rong & Xu, Changjin & Ahmad, Shabir & Li, Ying & Akgül, Ali, 2023. "Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Zhokh, O.O. & Strizhak, P.E., 2026. "A review of non-fickian reaction-diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    4. Shuai Yang & Qing Wei & Lu An, 2022. "Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository," Mathematics, MDPI, vol. 10(14), pages 1-7, July.
    5. Guo, Liujie & Gao, Fei & Zhan, Hui, 2022. "Existence, uniqueness and L∞-bound for weak solutions of a time fractional Keller-Segel system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Nazim I. Mahmudov, 2022. "Analytical Solution of the Fractional Linear Time‐Delay Systems and their Ulam‐Hyers Stability," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    8. Qiu, Lin & Chen, Wen & Wang, Fajie & Lin, Ji, 2019. "A non-local structural derivative model for memristor," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 169-177.
    9. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    10. Fang, Xinlei & Liang, Jianguo & Xie, Jiaquan & Chen, Zhanchun & Wu, Ting & Liu, Jianglin, 2025. "Dynamic analysis of the nonlinear fiber oscillator with fractional-order control in multi-filament fiber winding," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    11. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    12. Zhang, Yong & Yu, Xiangnan & Sun, HongGuang & Tick, Geoffrey R. & Wei, Wei & Jin, Bin, 2020. "Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

    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:jnlamp:v:2023:y:2023:i:1:n:6646284. 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/3197 .

    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.