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Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives

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Fractional Derivatives with Mittag-Leffler Kernel

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 194))

Abstract

The concentration of alcohol in blood differs with vessel diameter (arterial diameter). In case of arteries having thinner diameter, alcohol concentrates around their walls because of Fahraeus–Lindqvist effect. The fluctuating concentration of alcohol in blood directly affects normal human body functions causing peptic ulcer and hypertension. In this work, we made the comparative analysis of blood alcohol model via Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. The governing ordinary differential equations of blood alcohol model have been converted in terms of non-integers order derivatives. The analytic calculations of the concentrations of alcohol in stomach \((C_1(t))\) and the concentrations of alcohol in the blood \((C_2(t))\) have been investigated by applying Laplace transform method. The general solutions of the concentrations of alcohol in stomach \((C_1(t))\) and the concentrations of alcohol in the blood \((C_2(t))\) are expressed in the terms of wright function \(\varPhi (a,b;c)\). The graphs of both types of concentrations are depicted on the basis of fractional parameters of Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. Finally, the comparative analysis of both fractional types of concentration of alcohol level in blood decay faster for higher fractional order.

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Acknowledgements

The authors are highly thankful and grateful to Mehran university of Engineering and Technology, Jamshoro, Pakistan for generous support and facilities of this research work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro

  2. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Interna del Internado, Palmira, 62490, Cuernavaca, Morelos, México

    J. F. Gómez-Aguilar

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  1. Kashif Ali Abro
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  2. J. F. Gómez-Aguilar
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Correspondence to J. F. Gómez-Aguilar .

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Editors and Affiliations

  1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    José Francisco Gómez

  2. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  3. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    Ricardo Fabricio Escobar

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Abro, K.A., Gómez-Aguilar, J.F. (2019). Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives. In: Gómez, J., Torres, L., Escobar, R. (eds) Fractional Derivatives with Mittag-Leffler Kernel. Studies in Systems, Decision and Control, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-030-11662-0_5

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11661-3

  • Online ISBN: 978-3-030-11662-0

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