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

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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)

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.

Suggested Citation

  • M. M. Khader & Khaled. M. Saad, 2020. "Numerical treatment for studying the blood ethanol concentration systems with different forms of fractional derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-13, January.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:03:n:s0129183120500448
    DOI: 10.1142/S0129183120500448
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    Citations

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    Cited by:

    1. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Hari Mohan Srivastava & Khaled M. Saad, 2020. "A Comparative Study of the Fractional-Order Clock Chemical Model," Mathematics, MDPI, vol. 8(9), pages 1-14, August.

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