Maya Rayungsari, Raqqasyi Rahmatullah Musafir, Dian Savitri
In this article, we consider the memory effects, the Allee effect on prey, and predator cannibalism in a predator-prey model. The memory effect is represented by applying the Caputo-type fractional derivative to the model. The fundamental properties of the model have been investigated. The model have coexistence, predator-extinction, prey-extinction, and trivial equilibrium points. These four equilibrium points are asymptotically stable (both locally and globally) under certain conditions. The memory effect extends the local stability region of the coexistent point. Meanwhile, the Allee effect influences the possibility of the trivial point being asymptotically stable. Numerical simulations confirm the stability of each equilibrium point and show that the smaller the derivative order, the slower the solution converges to the equilibrium point. © 2025 Author(s).
Mathematics Education Study Program, Universitas PGRI Wiranegara, Pasuruan, 67118, Indonesia; Department of Mathematics, University of Brawijaya, Malang, 65145, Indonesia; Department of Mathematics, Universitas Negeri Surabaya, Surabaya, 60292, Indonesia
