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.

近年来，人们提出了许多新颖的分数导数定义，并将其用于生成具有记忆，背景或非局部效应的数学模型，以用于各种实际结构。本文的主要目的是为葡萄糖-胰岛素调节的广泛调节方案创建和评估分数阶导数。存在性和唯一性由不动点定理和迭代方案确定。我们建议使用脉冲微分方程模型研究患有脉冲胰岛素注射的糖尿病患者的血糖控制。它被认为是与糖尿病分数导数有关的确定性数学模型。对于小数订单，进行了数值模拟，以证明改变分数阶以达到理论结果的影响，并与Caputo导数进行了比较。这些案例研究的结果表明，这种分数阶模型的血浆葡萄糖控制是合适的候选者。