A Caputo (discretization) fractional-order model of glucose-insulin interaction: numerical solution and comparisons with experimental data

被引:37
作者
Alshehri, Mansoor H. [1 ]
Duraihem, Faisal Z. [1 ]
Alalyani, Ahmad [2 ]
Saber, Sayed [3 ,4 ]
机构
[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia
[2] Albaha Univ, Coll Sci & Arts Almandaq, Dept Math, Albaha, Saudi Arabia
[3] Beni Suef Univ, Dept Math & Comp Sci, Fac Sci, Bani Suwayf, Egypt
[4] Albaha Univ, Fac Sci & Arts Baljurashi, Dept Math, Albaha, Saudi Arabia
关键词
Caputo (discretization) fractional-order model; IVGTT; glucose-insulin interaction;
D O I
10.1080/16583655.2021.1872197
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, we investigate a (discretization) Caputo fractional glucose-insulin model qualitatively with incommensurate orders that appear in Bergman's minimal model. After intravenous tolerance testing, the model is used to characterize the blood insulin and glucose metabolism. We also prove that the presented model possesses existence, uniqueness, non-negative, and boundedness solution. We also proceed a systematical studies on the stability of the (discretization) Caputo fractional. Comparisons between the results of the fractional-order, the integer order and the measured real data obtained from patients are presented. These comparisons is shown that the presented Caputo fractional order model is better representative of the system than its integer order form. Numerical solutions of the Caputo fractional model are obtained by using the method of Adams-Bashforth-Moulton type to handle the fractional derivatives. Also, numerical simulations of the discretization fractional derivative order model are used to support the analytical results.
引用
收藏
页码:26 / 36
页数:11
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