Stability and Intelligent Control of a Fractional Predator–Prey System with Time Delay and Holling Type-III Functional Response

This paper presents an analytical and control model for a fractional-order delayed predator–prey system with a Holling Type-III functional response. In the model, Caputo fractional derivatives capture long-term memory and hereditary effects in population dynamics, while the finite-delay terms model gestation and environmental feedback processes. Analytical formulations prove the existence, uniqueness, positivity, and boundedness of solutions using fractional comparison lemmas and generalized Grönwall-type inequalities, yielding biologically plausible solutions. Afterward, a synergetic approach to intelligent control is used in order to stabilize the nonlinear fractional system with parametric uncertainties and external perturbations. The controller makes use of an adaptive intelligent estimator that is used to recover unknown dynamics and provide asymptotically stable equilibrium states. Moreover, bifurcation and directional dynamic studies are being conducted to define the impacts of fractional order and delay on the system stability and rich dynamical transitions, and multi-stability regions are observed. The model framework combines the concepts of fractional calculus, delayed nonlinear interactions, and intelligent control and provides some novel information about the modeling and stabilization of complex memory-dependent dynamical systems. The research plays a significant role in climate action, life on land, and life below water.