A control of glucose level in insulin therapies for the development of artificial pancreas by Atangana Baleanu derivative

Abstract

In this paper, we analyze the fractional modeling of diabetes mellitus model using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, The primary aim of this article is to create and evaluate a fractional order derivatives system for an extensive regulatory scheme of glucose insulin regulation for glucose insulin pump to control diabetes. The existence and uniqueness are determined by fixed point theorem and an iterative scheme. We suggest an impulsive differential equation model to study plasma glucose control for diabetic patients with impulsive insulin injections and by measuring the glucose level which leads to normal level in finite time. It is regarded as deterministic fractional derivative model related to the diabetes mellitus which provide the better control strategy at fractional values for the development of artificial pancreas. For different fractional orders, numerical simulations are performed to demonstrate the impacts of varying the fractional order to achieve the theoretical outcomes and comparison is made for the caputo and caputo fabrizio derivative. The results of these case studies by controlling plasma glucose with fractional order model makes it an appropriate candidate to control the type 1 diabetes in human.