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Master–slave synchronization for glucose–insulin metabolism of type-1 diabetic Mellitus model based on new fractal–fractional order derivative

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  • Babu, N. Ramesh
  • Balasubramaniam, P.

Abstract

Type-1 diabetes mellitus (T1DM) is one of the most extensive diseases in the world. In this disorder, a malfunction occurs in the glucose–insulin regulatory system when one intakes food. Therefore, the synchronization of T1DM and perturbed T1DM models are necessary to transform the disturbance behavior of T1DM into a typical T1DM model. In this paper, a type-1 diabetic mellitus glucose–insulin metabolism (T1DMGIM) model is concerned with a new fractal–fractional operator β∈(0,1],η∈(0,1] by adding food intake as a disturbance to the plant system. A new generalized differentiation operator is introduced as the convolution of the power law. This new operator is based on the fractal–fractional differentiation and integration operators in the Riemann–Liouville (R-L) sense. Sufficient conditions are achieved for the existence, uniqueness, and stability of an error T1DMGIM model by employing the Mönch contraction principle. Finally, numerical simulations are provided to verify the theoretical results.

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  • Babu, N. Ramesh & Balasubramaniam, P., 2023. "Master–slave synchronization for glucose–insulin metabolism of type-1 diabetic Mellitus model based on new fractal–fractional order derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 282-301.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:282-301
    DOI: 10.1016/j.matcom.2022.08.014
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    References listed on IDEAS

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    Cited by:

    1. Admon, Mohd Rashid & Senu, Norazak & Ahmadian, Ali & Majid, Zanariah Abdul & Salahshour, Soheil, 2024. "A new modern scheme for solving fractal–fractional differential equations based on deep feedforward neural network with multiple hidden layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 311-333.
    2. Farman, Muhammad & Ahmad, Aqeel & Zehra, Anum & Nisar, Kottakkaran Sooppy & Hincal, Evren & Akgul, Ali, 2024. "Analysis and controllability of diabetes model for experimental data by using fractional operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 133-148.

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