Glucose-insulin regulatory system: Chaos control and stability analysis via Atangana–Baleanu fractal-fractional derivatives

Abstract

This study explores the glucose-insulin regulatory system using a fractal-fractional framework based on the Atangana–Baleanu derivative. By formulating a set of differential equations incorporating the Atangana–Baleanu fractal-fractional derivative, we capture the intricate, nonlinear dynamics of glucose and insulin. This is with enhanced accuracy compared to traditional models. We establish the existence and uniqueness of solutions through fixed-point theory and analyze Hyers–Ulam stability. Moreover, we employ a linear controller to stabilize chaotic behavior in the system, mitigating fluctuations that can lead to erratic physiological responses. Both analytical and numerical results validate the model’s robustness to representing physiological processes. Our findings demonstrate that the fractal-fractional model significantly improves glucose-insulin dynamics modeling, highlighting its potential as a powerful tool for diabetes management and prediction of complex biological behaviors.