A Fractional Lotka–Volterra Predator–Prey Model with Strong Allee Effects, Nonlinear Harvesting, and Memory

This work develops a fractional Lotka–Volterra predator–prey model incorporating a strong Allee effect, nonlinear anthropogenic harvesting, and memory-dependent dynamics through the Atangana–Baleanu–Caputo (ABC) fractional operator. The model describes the interactions between two prey populations and a predator under competition, predation, and nonlinear harvesting. Theoretical analysis establishes the existence and uniqueness, non-negativity, ultimate boundedness, and Ulam–Hyers stability of the solutions. Numerical simulations examine the effects of the fractional order ϖ, the characteristic time-scale τ, the Allee-effect parameters, and harvesting effort. The results show that the fractional order modifies transient population dynamics, while τ regulates the fractional response through the factor τ1−ϖ. A systematic analysis of the Allee threshold C1 reveals a sharp numerical persistence and extinction transition for the stronger prey, bracketed within 12.448