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  4. Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative

Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative

MMC.
2024;
Volume 11, Number 1
: pp. 166–177
https://doi.org/10.23939/mmc2024.01.166
Received: June 22, 2023
Revised: February 06, 2024
Accepted: February 11, 2024

Assadiki F., El Younoussi M., Hattaf K., Yousfi N. Dynamics of an ecological prey–predator model based on the generalized Hattaf fractional derivative.  Mathematical Modeling and Computing. Vol. 11, No. 1, pp. 166–177 (2024)

Authors:
  1. F. Assadiki
  2. M. El Younoussi
  3. K. Hattaf
  4. N. Yousfi
1
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca
2
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca
3
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, Casablanca, Morocco; Centre Régional des Métiers de l'Education et de la Formation (CRMEF), Casablanca, Morocco
4
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca

In this paper, we propose and analyze a fractional prey–predator  model with generalized Hattaf fractional (GHF) derivative.  We prove that our proposed model is ecologically and mathematically well-posed.  Furthermore, we show that our model has three equilibrium points.  Finally, we establish the stability of these equilibria.

ecology
mathematical modeling
prey–predator
Hattaf fractional derivative
Lyapunov function
stability
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