Akademik Veri Yönetim Sistemi
International Journal of Applied and Computational Mathematics, cilt.11, sa.4, 2025 (Scopus)
This study explores a fractional predator–prey system employing the Caputo fractional derivative to account for memory effects inherent in biological systems. Notably, we extend the traditional fear effect model to include carry-over effects, reflecting the influence of past experiences on current prey behavior. Moreover, we consider the prey’s growth to be subject to the double Allee effect. The stability and bifurcation analysis of the proposed model is made. Our findings indicate that the fractional order significantly impacts the system’s stability, providing insights into the complex interplay between memory and ecological interactions. This research contributes to a deeper comprehension of predator–prey dynamics and offers a novel approach to modeling ecological systems with memory effects. Numerical simulations are provided to illustrate the theoretical results and their biological implications.