A Crossover Optimal Control Framework for a Time‐Delayed Fractional‐Order Diabetes Model: Stability, Bifurcation, and Numerical Analysis

This study introduces a novel crossover optimal control framework for a time‐delayed fractional‐order mathematical model of diabetes. We begin by developing a fractional‐order model with a time delay and conducting a comprehensive stability analysis of its steady states, followed by a detailed bifurcation analysis. Next, we propose a fractional‐order diabetes control model, where the control variable is designed to regulate blood glucose levels by managing insulin dynamics. This control model is further extended into a crossover framework, incorporating variable‐order and fractional‐order operators defined in the Caputo sense. To solve the resulting crossover time delay optimality system numerically, we employ a discretization approach based on the nonstandard finite difference method and the Grünwald–Letnikov scheme. Numerical simulations and comparative studies are provided to validate the effectiveness and demonstrate the simplicity of the proposed approximation method. The primary finding of this study indicates that the crossover‐controlled system is the most effective approach for regulating blood glucose levels and managing diabetes.