A Caputo Fabrizio fractional order model for control of glucose in insulin therapies for diabetes

Abstract

Many fresh definitions of fractional derivatives have been suggested and used in recent years to produce mathematical models with memory, background, or non-local effects for a broad range of real-world structures. The primary aim of this article is to create and evaluate a fractional-order derivative for an extensive regulatory scheme for glucose-insulin regulation. The existence and uniqueness are determined by a fixed point theorem and an iterative scheme. We suggest an impulsive differential equation model study plasma glucose control for diabetic patients with impulsive insulin injections. It is regarded as a deterministic mathematical model related to the diabetes mellitus fractional derivatives. For fractional orders, numerical simulations are performed to demonstrate the impacts of varying the fractional-order to achieve the theoretical outcomes and comparison with the Caputo derivative are made. The results of these case studies indicate that this plasma glucose control of the fractional-order model is an appropriate candidate.