A Caputo (Discretization) Fractional-Order Model Of Glucose-Insulin Interaction: Numerical Solution And Comparisons With Experimental Data

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.