Analytical solutions and physical interpretation of a predator–prey system with Allee effect using fractional derivative operators

Günhan Ay N., YAŞAR E.

Partial Differential Equations in Applied Mathematics, cilt.11, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.padiff.2024.100785
  • Dergi Adı: Partial Differential Equations in Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Anahtar Kelimeler: Bäcklund transformation approach, Exact solution, Fractional derivative operators, Generalized exponential function method, Predator–prey system
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

This study investigates the dynamics of a predator–prey system by incorporating the Allee effect. The exact analytical solutions of the system are explored using the generalized exponential function method and the Bäcklund transformation approach. The system is discussed using Conformable, M-truncated, and Beta time fractional derivative operators to provide a physical interpretation. The effects of these derivative operators on the solutions are demonstrated through various 2D and 3D graphical simulations. Furthermore, the impacts of physical parameters on the model are analysed, providing valuable insights into the dynamics of Predator–prey systems with the Allee effect. Our obtained solutions differ from those in the literature, owing to the methodologies employed and the choice of differential operators utilized. Nevertheless, we believe that the comparisons presented for the differential operators are effective and beneficial.