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Analysis of fractional blood alcohol model with composite fractional derivative

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  • Singh, Jagdev

Abstract

The present article deals with certain new and interesting features of fractional blood alcohol model associated with powerful Hilfer fractional operator. The solution of the model depends on three parameters such as (i) the initial concentration of alcohol in stomach after ingestion (ii) the rate of alcohol absorption into the blood stream (ii) the rate at which the alcohol is metabolized by the liver. By employing Sumudu transform algorithm the analytic results of the concentration of alcohol in stomach and the concentration of alcohol in the blood are analyzed. The general solution of concentration of alcohol in stomach and the concentration of alcohol in the blood are demonstrated in the form of extended Mittag-Leffler function. The effect of fractional parameter on concentration of alcohol in stomach and the concentration of alcohol in the blood are shown in graphical form. The comparative study for both the concentrations shows the new features of composite fractional derivative in the discussed model. The discussed fractional blood alcohol model yields important and useful results to interpolate new information in the direction of medical environment.

Suggested Citation

  • Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305233
    DOI: 10.1016/j.chaos.2020.110127
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    1. 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.
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    4. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Nisar, Kottakkaran Sooppy & Singh, Jagdev, 2020. "Fractional modified Kawahara equation with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    6. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    7. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    8. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    9. Fazli, Hossein & Nieto, Juan J., 2018. "Fractional Langevin equation with anti-periodic boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 332-337.
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    6. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Wedad Albalawi & Rasool Shah & Nehad Ali Shah & Jae Dong Chung & Sherif M. E. Ismaeel & Samir A. El-Tantawy, 2023. "Analyzing Both Fractional Porous Media and Heat Transfer Equations via Some Novel Techniques," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    8. Oliver Stark & Marius Eckert & Albertus Johannes Malan & Sören Hohmann, 2022. "Fractional Systems’ Identification Based on Implicit Modulating Functions," Mathematics, MDPI, vol. 10(21), pages 1-24, November.
    9. Omame, A. & Abbas, M. & Onyenegecha, C.P., 2021. "A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    10. Izadi, Mohammad & Srivastava, H.M., 2021. "Numerical approximations to the nonlinear fractional-order Logistic population model with fractional-order Bessel and Legendre bases," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    12. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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