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Journal of Environmental Accounting and Management 14(1) (2026) 61--85 | DOI:10.5890/JEAM.2026.03.006

Aqeel Ahmad$^{1,2}$, Shah Jahan$^3$, Muhammad Farman$^{2,4,5}$, Qurat Ul Ain$^1$, Abdul Ghaffar$^1$,\\ Aceng Sambas$^{4,6,7}$

$^1$ Department of Mathematics, Ghazi University D G Khan 32200, Pakistan

$^2$ Faculty of Arts and Sciences, Department of Mathematics, Near East University, Turkey

$^3$ Institute of Mathematics,Khwaja Fareed University of Engineering and Information Technology, Raheem Yar Khan, Pakistan

$^4$ Faculty of Arts and Sciences, Department of Mathematics, Near East University, Turkey

$^5$ Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan

$^6$ Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tamansari Gobras 46196 Tasikmalaya, Indonesia

$^7$ Artificial Intelligence for Sustainability and Islamic Research Center (AIRIS), Universiti Sultan Zainal Abidin, Gongbadak, Terengganu, 21300, Malaysia

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Abstract

This study's objective is to assess and manage diabetes by combining glucagon measurements. A new mathematical model is created based on the obtained novel hypothesis by combining glucagon and therapy. To ascertain the stable status of the recently constructed system which is analysis both qualitatively and quantitatively to understand the dynamics of control under bounded domain. Stability analysis have been derived on local as well as global scale using Lyapunov's first derivative functions to evaluate the overall effects of disease propagation and control. Existence and positive solutions properties are also derived under non-local operator our proposed model and retains the properties of Schauder’s and Krasnoselski’s theorems. To ensure reliable bounded findings, the boundedness and uniqueness are examined, those are necessary characteristics for non-epidemic models. We use Lipschit'z conditions and linear growth to fully validate the global derivative that characterizes the rate of change of disease impact on each sub-compartment. The bounded numerical solutions for for proposed model using Mittag-Leffler kernel with fractal fractional operator at fractional order values. A number of variables are imposed with continuous monitoring, and simulations are created using MATLAB coding to see the actual effects of diabetes spread and control with the glucagon effect regularised the glucose insulin level.

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