(untitled) (Journal of Mathematical Modeling and Fractional Calculus, 2026)
In this study, we propose and analyze a novel fractional-order preypredator-super predator model that incorporates maturation delay, harvesting, and the Allee effect. The prey population is assumed to grow logistically under the influence of a strong Allee effect, with a time delay accounting for the mat uration period. Predators and super predators interact through predation and competition, while also experiencing harvesting impacts. The system is described using the Caputo fractional derivative to bet ter capture memory effects inherent in ecological processes. Furthermore, herd behavior in predation is represented through a generalized functional response dependent on a parameter α, modeling various herd structures such as circular, square, cubic, and spherical formations. Key parameters include the intrinsic growth rate of prey, carrying capacity, mortality rates, predation coefficients, Allee threshold, and harvesting intensities. We investigate the existence and local stability of equilibria, derive the net reproduction numbers for both predator and super predator populations, and perform a Hopf bifurca tion analysis to explore the emergence of delay-induced periodic solutions. The results enhance the understanding of how memory, delay, harvesting, and Allee effects collectively influence the dynamics of ecological systems. The AdamsBashforthMoulton method is employed to approximate the solutions of the proposed model. Using Python, we perform graphical illustrations and numerical simulations to support our analysis.