Investigation of fractional diabetes model involving glucose–insulin alliance scheme

• Published in: International journal of dynamics and control Vol. 12; no. 1; pp. 1 - 14
• Main Authors: Khirsariya, Sagar R., Rao, Snehal B., Hathiwala, Gautam S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024; Springer Nature B.V
• Subjects: Complexity; Control; Control and Systems Theory; Diabetes; Diabetes mellitus; Dynamical Systems; Engineering; Existence theorems; Fixed points (mathematics); Glucose; Homotopy theory; Insulin; Laplace transforms; Mathematical models; Stability analysis; Vibration; 92Dxx; 92Bxx; Adomian decomposition Laplace transform method; Atangana–Baleanu fractional derivative; 26A33; Fractional diabetes model; Stability analysis; 34A08
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-023-01293-4

The ultimate aim of this study is to develop and analyze a comprehensive regulatory framework for managing glucose and insulin in blood in the presence of diabetes mellitus. This innovative mathematical model of diabetes is demonstrated and examined in fractional order by involving ABC fractional derivative. This whole framework is worked out using a semi-analytical technique, namely the Adomian decomposition Laplace transform method. To prove the efficiency of this ADLTM technique, the results are compared with other classical methods, viz. homotopy perturbation transform method and modified homotopy analysis transform method. Using the Banach fixed point theorem, the existence and stability analysis of the solution has been proved. Certain figures and tables are illustrated for this fractional diabetes model with some fractional order. We used the Maple software to generate all the numerics and graphical plots. This detailed investigation also explores how well the level of glucose and insulin affects the dynamics of disease infection.