IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p330-d1572388.html
   My bibliography  Save this article

On the Extended Simple Equations Method (SEsM) and Its Application for Finding Exact Solutions of the Time-Fractional Diffusive Predator–Prey System Incorporating an Allee Effect

Author

Listed:
  • Elena V. Nikolova

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

Abstract

In this paper, I extend the Simple Equations Method (SEsM) and adapt it to obtain exact solutions of systems of fractional nonlinear partial differential equations (FNPDEs). The novelty in the extended SEsM algorithm is that, in addition to introducing more simple equations in the construction of the solutions of the studied FNPDEs, it is assumed that the selected simple equations have different independent variables (i.e., different coordinates moving with the wave). As a consequence, nonlinear waves propagating with different wave velocities will be observed. Several scenarios of the extended SEsM are applied to the time-fractional predator–prey model under the Allee effect. Based on this, new analytical solutions are derived. Numerical simulations of some of these solutions are presented, adequately capturing the expected diverse wave dynamics of predator–prey interactions.

Suggested Citation

  • Elena V. Nikolova, 2025. "On the Extended Simple Equations Method (SEsM) and Its Application for Finding Exact Solutions of the Time-Fractional Diffusive Predator–Prey System Incorporating an Allee Effect," Mathematics, MDPI, vol. 13(3), pages 1-31, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:330-:d:1572388
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/330/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/330/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Ryu, Kimun & Ko, Wonlyul, 2019. "Asymptotic behavior of positive solutions to a predator–prey elliptic system with strong hunting cooperation in predators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    3. Vahid Reza Hosseini & Arezou Rezazadeh & Hui Zheng & Wennan Zou, 2022. "A Nonlocal Modeling For Solving Time Fractional Diffusion Equation Arising In Fluid Mechanics," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-21, August.
    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. Emmanuel Yomba & Poonam Ramchandra Nair, 2024. "New Coupled Optical Solitons to Birefringent Fibers for Complex Ginzburg–Landau Equations with Hamiltonian Perturbations and Kerr Law Nonlinearity," Mathematics, MDPI, vol. 12(19), pages 1-29, September.
    2. Sivalingam, S M & Kumar, Pushpendra & Trinh, Hieu & Govindaraj, V., 2024. "A novel L1-Predictor-Corrector method for the numerical solution of the generalized-Caputo type fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 462-480.
    3. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.
    5. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a time fractional advection-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Djilali, Salih & Cattani, Carlo, 2021. "Patterns of a superdiffusive consumer-resource model with hunting cooperation functional response," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    7. Bonyah, Ebenezer & Akgül, Ali, 2021. "On solutions of an obesity model in the light of new type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    8. Arfaoui, Hassen & Ben Makhlouf, Abdellatif, 2022. "Stability of a fractional advection–diffusion system with conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Zulqurnain Sabir & Thongchai Botmart & Muhammad Asif Zahoor Raja & Wajaree Weera, 2022. "An advanced computing scheme for the numerical investigations of an infection-based fractional-order nonlinear prey-predator system," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-13, March.

    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:13:y:2025:i:3:p:330-:d:1572388. 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.