https://doi.org/10.1140/epjp/s13360-020-00420-w
Regular Article
Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative
1
Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, Balıkesir, Turkey
2
Department of Mathematics, Faculty of Arts and Sciences, Mehmet Akif Ersoy University, Burdur, Turkey
3
Department of Medical Pathology, Faculty of Medicine, Balıkesir University, Balıkesir, Turkey
* e-mail: sumeyraucar@balikesir.edu.tr
Received:
21
March
2020
Accepted:
27
April
2020
Published online:
19
May
2020
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 
-cells.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
