Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator
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Date
2023-09
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Abstract
This article aims to introduce and analyze a diabetes mellitus model of fractional order, utilizing the ABC
derivative. Diabetes mellitus is a prevalent and significant disease worldwide, ranking among the top causes
of mortality. It is characterized by chronic metabolic dysfunction, leading to elevated blood glucose levels
and subsequent damage to vital organs including the nerves, kidneys, eyes, blood vessels, and heart. The
fractional ABC derivative is used in this study to describe and analyzediabetes mellitus mathematically while
removing hereditary influences. The investigation begins by exploring the initial points of the diabetes mellitus
model. Under the fractional ABC operator, Picard’s theorem is used to prove the existence and uniqueness of
solutions. For the numerical approximation of solutions in the fractional-order diabetes mellitus model, this
study used a specialized technique that combines the principles of fractional calculus and a two-step Lagrange
polynomial interpolation. Finally, the obtained results are visually presented through graphical representations,
serving as empirical evidence to support our theoretical findings. The numerical experiments showed that the
proportion of patients with diabetes mellitus increased as the fractional dimension (𝜃) reduced. The combination
of mathematical modelling, analysis, and numerical simulations provides insights into the dynamics of diabetes
mellitus, offering valuable contributions to the understanding and management of this prevalent disease.
Additionally, the proposed scheme can be enhanced by incorporating the ABC operator, allowing for the
simulation of real-world dynamics and behavior in the coexistence of diabetes mellitus and tuberculosis.