Abstract
The purpose of this paper is to implement an approximate method for obtaining the solution of a physical model called the blood ethanol concentration system. This model can be expressed by a system of fractional differential equations (FDEs). Here, we will consider two forms of the fractional derivative namely, Caputo (with singular kernel) and Atangana–Baleanu–Caputo (ABC) (with nonsingular kernel). In this work, we use the spectral collocation method based on Chebyshev approximations of the third-kind. This procedure converts the given model to a system of algebraic equations. The implementation of the proposed method to solve fractional models in ABC-sense is the first time. We satisfy the efficiency and the accuracy of the given procedure by evaluating the relative errors. The results show that the implemented technique is an easy and efficient tool to simulate the solution of such models.