Comparing the Numerical Solution of Fractional Glucose–Insulin Systems Using Generalized Euler Method in Sense of Caputo, Caputo–Fabrizio and Atangana–Baleanu

Abstract

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated with changes in beta-cell kinetics. We discuss the solution to the problem with respect to its existence, uniqueness, non-negativity, and boundedness. Using three different fractional derivative operators, the proposed model is examined. To approximate fractional-order systems, we use an efficient numerical Euler method in Caputo, Caputo–Fabrizio, and Atangana–Baleanu sense. Several asymptomatic behaviors are observed in the proposed models based on these three operators. These behaviors do not appear in integer-order derivative models. These behaviors are essential for understanding fractional-order systems dynamics. Our results provide insight into fractional-order systems dynamics. These operators analyze local and global stability and Hyers–Ulam stability. Furthermore, the numerical solutions for the proposed model are simulated using the three methods.

Keywords

• glucose–insulin
• Euler method
• Caputo
• Caputo–Fabrizio
• Atangana–Baleanu operators
• local and global stability