A Modified Variation Iteration Method for the Fractional-Order Glucose-Insulin Regulatory Model: Stability Analysis and Numerical Simulation

Abstract

This study presents a novel semi-analytical approach based on the Modified Variation Iteration Method (MVIM) for solving the fractional-order glucose-insulin regulatory model proposed by Sandhya and Kumar. The proposed method employs Caputo–Fabrizio fractional derivatives, which provide a more realistic representation of the glucose-insulin reaction dynamics. The MVIM offers efficient computation and rapid convergence and is particularly well-suited for nonlinear biological systems, yielding accurate approximations with minimal computational effort. A stability analysis of the fractional-order glucose-insulin regulatory (FGIR) system was performed to determine the conditions under which physiological equilibrium was preserved. Numerical simulations were conducted to validate the theoretical findings and assess the influence of varying fractional orders on glucose and insulin levels. The results demonstrate that the proposed methodology provides considerable modeling flexibility and effectively captures the long-term dependencies inherent in glucose-insulin regulation. Furthermore, the MVIMbased framework establishes a foundation for developing improved mathematical tools for stability analysis and diabetes management.