Numerical treatment for studying the blood ethanol concentration systems with different forms of fractional derivatives

M. M. Khader and Khaled. M. Saad
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M. M. Khader: Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia2Department of Mathematics, Faculty of Science, Benha University Benha, Egypt
Khaled. M. Saad: Department of Mathematics, College of Arts and Sciences, Najran University, Saudi Arabia4Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 03, 1-13

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.

Keywords: Blood ethanol concentration system; Atangana–Baleanu–Caputo fractional derivative; Chebyshev polynomials; spectral collocation method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0129183120500448

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