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Investigation of fractional diabetes model involving glucose–insulin alliance scheme

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Abstract

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.

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Acknowledgements

We would like to thank the editor and reviewers for their thoughtful and detailed comments on our article.

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Authors and Affiliations

  1. Department of Mathematics, Marwadi University, Rajkot-Morbi Road, Rajkot, Gujarat, 360003, India

    Sagar R. Khirsariya & Gautam S. Hathiwala

  2. Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, 390001, India

    Snehal B. Rao

Authors
  1. Sagar R. Khirsariya
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  2. Snehal B. Rao
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  3. Gautam S. Hathiwala
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Contributions

SRK has developed the method and wrote the initial draft of the manuscript with all graphical and tabular results. GSH has analyzed the data and helped in theoretical part. SBR has reviewed and revised the whole manuscript. All authors approved the final version of the manuscript.

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Correspondence to Sagar R. Khirsariya.

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Khirsariya, S.R., Rao, S.B. & Hathiwala, G.S. Investigation of fractional diabetes model involving glucose–insulin alliance scheme. Int. J. Dynam. Control 12, 1–14 (2024). https://doi.org/10.1007/s40435-023-01293-4

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  • DOI: https://doi.org/10.1007/s40435-023-01293-4

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