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RESEARCH ARTICLE

Application of Jumarie-Stancu Collocation Series Method and Multi-Step Generalized Differential Transform Method to fractional glucose-insulin

Sayed Saber1,2* ,  Brahim Dridi3 ,  Abdullah Alahmari3 ,  Mohammed Messaoudi4
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1 Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia
2 Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt
3 Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Saudi Arabia
4 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
IJOCTA, 025120054 https://doi.org/10.36922/IJOCTA025120054
Received: 19 March 2025 | Revised: 24 April 2025 | Accepted: 29 April 2025 | Published online: 20 May 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This study applies the Multi-Step Generalized Differential Transform Method (MSGDTM) and the Jumarie-Stancu Collocation Series Method (JSCSM) to analyze a fractional-order Model (1). The model incorporates Caputo fractional derivatives to capture the nonlocal and memory-dependent characteristics of glucose-insulin interactions, considering physiological factors such as β- cell activity and external glucose intake. Stability analysis reveals bifurcations and chaotic attractors, demonstrating the system’s sensitivity to fractional orders. Numerical simulations compare MSGDTM and JSCSM accuracy and efficiency, highlighting MSGDTM’s superior convergence and lower approximation error. The results show that fractional-order modeling provides a more accurate framework for understanding glucose-insulin dynamics and predicting metabolic behavior. Furthermore, control mechanisms are introduced to mitigate chaos, offering potential strategies for managing diabetes. This work emphasizes the robustness of MSGDTM in solving complex fractional biological models. It provides insights into fractional calculus applications in biomedical research.

Keywords
Fractional calculus
Glucose-insulin model
Numerical methods
Chaos control
Numerical simulation
MSGDTM
JSCSM
Funding
This research work was funded by Umm Al-Qura University, Saudi Arabia, under Grant No. 25UQU4340608GSSR02.
Conflict of interest
The authors declare they have no competing interests.
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