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

Authors

  • Sayed Saber Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia. Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt
  • Brahim Dridi Mathematics Department, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah, 21955, Saudi Arabia
  • Abdullah Alahmari Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Saudi Arabia
  • Mohammed Messaoudi Imam Mohammed Ibn Saud Islamic University (IMSIU), College of Science Department of Mathematics and Statistics, Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6152

Keywords:

Fractional calculus , Glucose-insulin model, Chaos control, Stability analysis, Caputo fractional derivative, Numerical simulation, Diabetes modeling.

Abstract

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.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Sayed Saber, Brahim Dridi, Abdullah Alahmari, Mohammed Messaoudi

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How to Cite

Hyers-Ulam Stability and Control of Fractional Glucose-Insulin Systems. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6152. https://doi.org/10.29020/nybg.ejpam.v18i2.6152