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Discontinuity, Nonlinearity, and Complexity 15(4) (2026) 609--622 | DOI:10.5890/DNC.2026.12.010

M. Ait Ichou$^{1}$, Z. Hajhouji$^2$, K. Hattaf$^{2,3}$

$^1$ EMA Team, RST Laboratory, ESEFA, Ibnou Zohr University of Agadir, Morocco

$^2$ Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'Scik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco

$^3$ Equipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM), Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco

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Abstract

In this paper, a fractional model for glucose-insulin with beta cells is suggested. The model considered involves the new Hattaf mixed fractional (HMF) derivative incorporating well-known types, in particular, Caputo (C), Caputo-Fabrizio (CF), Atangana-Baleanu (AB) and generalized Hattaf fractional (GHF) derivatives. We obtain two theoretical results. Firstly, based on suitable assumptions, it is shown that there is a solution for the system in question. In addition, local stability is demonstrated. {Furthermore, an experimental validation of the model is conducted using real clinical glucose and insulin data, confirming the model's ability to closely replicate the observed physiological behavior and demonstrating the relevance of the proposed HMF formulation in capturing key features of glucose–insulin dynamics}. Finally, in order to confirm our conclusions, numerical simulations are carried out to demonstrate the local stability of the metabolism dynamics. The effectiveness of the proposed method in providing the best approximation of the fractional derivative parameters relies on the local stability of the metabolic dynamics.

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