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Stability Analysis and Solutions of a Fractional-Order Model for the Glucose-Insulin Homeostasis in Rats

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Transactions on Engineering Technologies (IMECS 2018)

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Abstract

The main objectives of this works are to introduce a fractional order model of the glucose-insulin homeostasis in rats, to establish conditions for which an equilibrium point of the model is asymptotically stable, and to apply standard methods to solve the model for solutions. The exact solutions of the fractional-order model are derived using the Laplace transform. In particular, we apply the Laplace-Adomian- Padé method (LAPM), which is based on the Laplace-Adomian decomposition method (LADM), and the Adams-Bashforth-Moulton type predictor-corrector scheme to solve the model for analytical and numerical solutions, respectively. Moreover, the obtained exact solutions of this fractional-order model are employed to numerically and graphically compare with the results obtained using the proposed two methods. The LAPM and the predictor-corrector scheme can also be applied simply and efficiently to other fractional-order differential systems arising in engineering and applied mathematics problems.

S. Sirisubtawee and S. Koonprasert—Researchers in the Centre of Excellence in Mathematics, Bangkok, 10400, Thailand.

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Acknowledgements

This research is supported by the Department of Mathematics, King Mongkut’s University of Technology North Bangkok, Thailand and the Centre of Excellence in Mathematics, the Commission on Higher Educaton, Thailand.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Natchapon Lekdee, Sekson Sirisubtawee & Sanoe Koonprasert

Authors
  1. Natchapon Lekdee
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  2. Sekson Sirisubtawee
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  3. Sanoe Koonprasert
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Corresponding author

Correspondence to Sekson Sirisubtawee .

Editor information

Editors and Affiliations

  1. International Association of Engineers, Hong Kong, Hong Kong

    Sio-Iong Ao

  2. Department of Computer and Communication, Dae Gu Catholic University, Daegu, Korea (Republic of)

    Haeng Kon Kim

  3. Graduate Division, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  4. Department of SEEM, City University of Hong Kong, Kowloon, Hong Kong

    Alan Hoi-shou Chan

  5. Department of Industrial Engineering and Management, Kanagawa University, Yokohama, Japan

    Hideki Katagiri

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Lekdee, N., Sirisubtawee, S., Koonprasert, S. (2020). Stability Analysis and Solutions of a Fractional-Order Model for the Glucose-Insulin Homeostasis in Rats. In: Ao, SI., Kim, H., Castillo, O., Chan, As., Katagiri, H. (eds) Transactions on Engineering Technologies. IMECS 2018. Springer, Singapore. https://doi.org/10.1007/978-981-32-9808-8_20

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