Numerical Solution of the Fractional-Order Mathematical Model of β-Cells Kinetics and Glucose-Insulin System Using a Predictor-Corrector Method

This paper is devoted to investigating the numerical solution of a nonlinear fractional-order mathematical model which combines both β-cells kinetics and a glucose-insulin feedback system. This nonlinear fractional-order mathematical model will describe changes in plasma glucose and insulin levels over time. We study the existence, uniqueness, nonnegativity and boundedness for the solution of the proposed fractional-order mathematical model. We also investigate the local and global stability of the proposed model. Numerical solution of the proposed model is computed and simulated by using the method of Adams–Bashforth–Moulton type. Numerical solution is demonstrated through an illustrative example and is carried out to illustrate and support the analytical results.