Analysis of a Fractional-order Glucose-Insulin Biological System with Time Delay

In the human glucose-insulin regulatory system, diverse metabolic issues can arise, including diabetes type I and II, hyperinsulinemia, hypoglycemia, etc. Therefore, analysis characterization of such a biological system is must. It well known that mathematical models are an excellent option to study predict natural phenomena some extent. On other hand, fractional-order calculus provides generalization derivatives integrals arbitrary orders giving us framework add memory properties extra degree freedom approximate real-world with higher accuracy. this work, we introduce version model system. Using Caputo derivative, investigate different concentration rates among insulin, glucose, healthy beta cells. Additionally, incorporates two time-lags represent elapsed time in insulin secretion response blood glucose level delay drop due increased concentration. Analytical results equilibrium points their corresponding stability given. Numerical results, phase portraits bifurcation diagrams, reveal increases chaotic regions, leading potential problems. Vice versa, seems work correctly when behavior evolves periodic windows.