<p>This study investigates the nonlinear dynamics of the glucose-insulin regulatory system using advanced fractional-order modeling that addresses the limitations of traditional integer-order models. Through the Caputo fractional derivative, the model captures long-term dependencies that are critical to understanding complex biological interactions. Two numerical methods are used to solve fractional differential equations: Adams-Bashforth-Moulton and Laplace-Adomian-Padé Method. This study compares these methods. With its predictor-corrector structure, the Adams-Bashforth-Moulton method offers superior accuracy, stability, and efficiency when handling chaotic and highly nonlinear dynamics. In contrast to Laplace-Adomian-Padé Method, Adams-Bashforth-Moulton has low residual errors and enhanced stability, whereas Laplace-Adomian-Padé Method is computationally efficient but has limitations in chaotic regimes. Furthermore, bifurcation analysis and Lyapunov exponents confirm chaotic oscillations, emphasizing the system’s sensitivity to parameter changes. Moreover, the researchers propose chaotic control strategies crucial for managing diabetes based on fractional-order modeling in biomedical systems.</p>