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Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative

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Abstract

Diabetes mellitus, at the forefront of the diseases of our age, is a type of disease that plays a leading role in the formation of many deadly diseases and is very common all over the world. In this work, based on the system in Shabestari et al. (Chaos Solitons Fractals 112:44–51, 2018), we give the fractional glucose–insulin regulatory system for the first time by Caputo–Fabrizio derivative. We present special solutions, stability analysis, uniqueness of the solution for this fractional system with the aid of Banach fixed point theory. Taking various values belonging to the fractional order into consideration, we present some numerical results according to the relation between glucose, insulin and \(\beta \)-cells.

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Acknowledgements

The authors would like to thank Asist. Prof. Dr. Beyza Billur Iskender Eroğlu for her valuable contributions to Sect. 8 of our study. This research is supported by Balikesir University Research Grant No. Bap 2019/098.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, Balıkesir, Turkey

    Sümeyra Uçar & Necati Özdemir

  2. Department of Mathematics, Faculty of Arts and Sciences, Mehmet Akif Ersoy University, Burdur, Turkey

    İlknur Koca

  3. Department of Medical Pathology, Faculty of Medicine, Balıkesir University, Balıkesir, Turkey

    Eren Altun

Authors
  1. Sümeyra Uçar
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  2. Necati Özdemir
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  3. İlknur Koca
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  4. Eren Altun
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Correspondence to Sümeyra Uçar.

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Uçar, S., Özdemir, N., Koca, İ. et al. Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative. Eur. Phys. J. Plus 135, 414 (2020). https://doi.org/10.1140/epjp/s13360-020-00420-w

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00420-w

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