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# Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative

Ravi Shanker Dubey1, Dumitru Baleanu2,3, Manvendra Narayan Mishra1,*, Pranay Goswami4

1 Department of Mathematics, AMITY School of Applied Science, AMITY University Rajasthan, Jaipur, 302022, India
2 Department of Mathematics and Computer Sciences, Cankaya University, Balgat, 06530, Turkey
3 Institute of Space Sciences, Magurele-Bucharest, R76900, Romania
4 School of Liberal Studies, Dr. B.R. Ambedkar University Delhi, Delhi, 110006, India

* Corresponding Author: Manvendra Narayan Mishra. Email:

(This article belongs to this Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics)

Computer Modeling in Engineering & Sciences 2021, 128(3), 1247-1263. https://doi.org/10.32604/cmes.2021.015224

## Abstract

Diabetes is a burning issue in the whole world. It is the imbalance between body glucose and insulin. The study of this imbalance is very much needed from a research point of view. For this reason, Bergman gave an important model named-Bergman minimal model. In the present work, using Caputo-Fabrizio (CF) fractional derivative, we generalize Bergman’s minimal blood glucose-insulin model. Further, we modify the old model by including one more component known as diet D(t), which is also essential for the blood glucose model. We solve the modified model with the help of Sumudu transform and fixed-point iteration procedures. Also, using the fixed point theorem, we examine the existence and uniqueness of the results along with their numerical and graphical representation. Furthermore, the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied. Finally, we draw the graphs of G(t), X(t), I(t), and D(t) for different values of . It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.

## Keywords

Dubey, R. S., Baleanu, D., Mishra, M. N., Goswami, P. (2021). Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative. CMES-Computer Modeling in Engineering & Sciences, 128(3), 1247–1263.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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