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Sayed Saber et.al. / IJOCTA, Vol.15, No.3, pp.464-482 (2025)
and nonlocal characteristics. Fractional-order govern transitions between equilibrium, oscilla-
glucose-insulin regulation is highlighted in this tory, and chaotic dynamics, providing insights
study. The model captures nonlocal and memory- into mechanisms such as β-cell stress, insulin pro-
dependent glucose-insulin interactions by incor- duction, and glucose feedback. Numerical simula-
porating fractional derivatives. This feature pro- tions demonstrated that MSGDTM outperforms
vides a more realistic representation of glucose JSCSM and other classical schemes in terms of
regulation than traditional integer-order models. accuracy, convergence speed, computational sta-
The behavior of the system is highly dependent bility, and efficient handling of nonlocal memory
on fractional orders and parameter variations. terms, particularly in capturing nonlinear and os-
In healthy physiological states, fractional orders cillatory behaviors over long time intervals and
close to α = 1 stabilize near equilibrium points. near chaotic regimes. The bifurcation and Lya-
However, for α < 1, the system exhibits oscilla- punov analyses further confirmed that fractional-
tory or chaotic behaviors, potentially mimicking order models reflect more realistic physiological
pathological conditions like insulin resistance or behavior compared to their integer-order counter-
glucose instability. This study provides valuable parts, with graphical results emphasizing system
insights into how deviations in physiological con- sensitivity to fractional order variations (α = 0.97
ditions can lead to metabolic disorders and how to 1.0) and validating the effectiveness of linear
fractional parameters influence system stability. control strategies in stabilizing chaotic fluctua-
The MSGDTM provides superior numerical ac- tions. Based on these findings, fractional model-
curacy, faster convergence, and greater computa- ing is important in reproducing realistic glucose-
tional efficiency compared to the JSCSM. It is insulin dynamics and informing improved dia-
particularly effective at handling nonlinear and betes treatment interventions. Although limita-
memory-dependent characteristics of fractional tions remain—such as the restricted range of sim-
glucose-insulin systems. As a result of lower ap- ulated fractional orders—the overall model re-
proximation errors, MSGDTM is a more reliable mains biologically consistent, with negative pa-
method for solving fractional differential equa- rameters interpreted as inhibitory or decay pro-
tions. Furthermore, this study explores how con- cesses. Looking ahead, we plan to extend the
trol mechanisms influence chaotic glucose-insulin analysis to broader ranges of fractional orders, in-
dynamics. A controlled system exhibits signifi- corporate stochastic perturbations and time-delay
cant improvements in stability, suggesting ther- effects, and integrate patient-specific clinical data
apeutic interventions to prevent metabolic disor- to enhance the model’s applicability for person-
ders. By using LE analysis and bifurcation di- alized treatment planning. This study highlights
agrams, diabetes management strategies can be the value of fractional calculus and the robust-
developed. Due to this, fractional-order modeling ness of MSGDTM as a powerful, adaptable tool
is becoming more important in biomedicine. Fur- for solving complex nonlinear biomedical systems.
thermore, it improves glucose-insulin dynamics to
design therapeutic strategies for diabetes manage- Acknowledgments
ment. To improve real-world application, stochas- The authors extend their appreciation to
tic effects, environmental influences, or adaptive Umm Al-Qura University, Saudi Arabia, for
control strategies might be incorporated. Fur- supporting this research under Grant No.
thermore, integrating patient-specific data could 25UQU4340608GSSR02.
enhance predictive modeling and optimize dia-
betes treatment. Funding

This research work was funded by Umm Al-
7. Conclusion Qura University, Saudi Arabia, under Grant No.
25UQU4340608GSSR02.
In this work, we investigated a Model (1) in-
corporating Caputo fractional derivatives to cap- Conflict of interest
ture memory effects and hereditary character-
istics inherent in biological systems, particu- The authors declare they have no competing in-
terests.
larly glucose-insulin interactions. Two advanced
numerical techniques—the MSGDTM and the
Author contributions
JSCSM—were employed to solve the model and
analyze its dynamic behavior. Through compre- Conceptualization: Sayed Saber, Brahim Dridi
hensive stability, bifurcation, and chaos analyses, Investigation: Sayed Saber, Abdullah Alahmari,
we identified key parameters (a 16 to a 21 ) that Mohammed Messaoudi
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