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

作　　者：Ravi Shanker Dubey Dumitru Baleanu Manvendra Narayan Mishra Pranay Goswami 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2021年第9期1247-1263,共17页工程与科学中的计算机建模（英文）

摘　　要：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 minimalmodel.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 modelwith the help of Sumudu transformand 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),andD(t)for different values ofτ.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.

关 键 词：Bergman minimal model blood glucose Caputo-Fabrizio fractional derivative uniqueness and existence fractional calculus 

分 类 号：O17[理学—数学]