@article{Alhazmi2025, 
author = {Muflih Alhazmi and Safa M. Mirgani and A. F. Aljohani and Sayed Saber},
title = {Numerical simulation of a fractional glucose-insulin model via successive approximation and ABM schemes},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {22817-22849},
keywords = {fractional derivatives, nonlinear equations, simulation, numerical results, iterative method, zoonotic disease},
url = {https://www.sciopen.com/article/10.3934/math.20251014},
doi = {10.3934/math.20251014},
abstract = {We developed a fractional-order glucose–insulin regulatory model in the Caputo sense to encode memory effects in metabolic dynamics. The three-equation nonlinear system employed component-wise fractional orders to represent heterogeneous memory depths across plasma glucose, insulin action, and secretion. We established well-posedness (existence, uniqueness), positivity, and boundedness, and assess local stability; oscillatory regimes were further examined via discrete-time Hopf conditions for the discretized dynamics. For computation, we implement the successive approximation method (SAM) and a fractional Adams–Bashforth–Moulton (ABM) predictor–corrector scheme. In head-to-head tests, ABM achieved lower residuals, better stability, and higher efficiency than SAM, with validation against frequently sampled intravenous glucose tolerance test (FSIGT) data and a global sensitivity analysis highlighting insulin responsiveness and glucose-threshold parameters as most influential. Residual analysis indicated that increasing the fractional order(s) toward the integer case reduced numerical error—for example, the representative state error    |  Δ  u  | decreased from    129.6 at    ν  =  0.5 to    34.1 at    ν  =  0.9. These results supported the clinical relevance of fractional-order modeling for improved diabetes management, parameter tuning, and control strategy design.}
}