Hyers-Ulam Stability and Control of Fractional Glucose-Insulin Systems

This paper presents a novel fractional-order model for glucose-insulin dynamics using the Caputo-Fabrizio (CF) derivative, which accounts for memory effects through its nonsingular exponential kernel. Existence and uniqueness of the solution are established via fixed point theory, and infinite series solutions are obtained using the Sumudu transform. Hyers-Ulam stability is analyzed to assess the system’s robustness against perturbations. A linear control strategy is introduced to regulate glucose levels, demonstrating potential for integration with real-time insulin delivery systems. Compared to classical integer-order models, the proposed approach provides improved accuracy, enhanced stability, and deeper insight into the chaotic behavior of glucose-insulin interactions. This framework supports the development of personalized diabetes treatment and adaptive control strategies.