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First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface

Author

Listed:
  • Muhammad Imran Asjad

    (Department of Mathematics, University of Management and Technology Lahore, Lahore 54770, Pakistan)

  • Saif Ur Rehman

    (Department of Mathematics, University of Management and Technology Lahore, Lahore 54770, Pakistan)

  • Ali Ahmadian

    (Institute of IR 4.0, The National University of Malaysia, Bangi 43600, Selangor, Malaysia)

  • Soheil Salahshour

    (Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul 34349, Turkey)

  • Mehdi Salimi

    (Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
    Center for Dynamics, Faculty of Mathematics, Technische Universitt Dresden, 01062 Dresden, Germany)

Abstract

The present study provides the heat transfer analysis of a viscous fluid in the presence of bioconvection with a Caputo fractional derivative. The unsteady governing equations are solved by Laplace after using a dimensional analysis approach subject to the given constraints on the boundary. The impact of physical parameters can be seen through a graphical illustration. It is observed that the maximum decline in bioconvection and velocity can be attained for smaller values of the fractional parameter. The fractional approach can be very helpful in controlling the boundary layers of the fluid properties for different values of time. Additionally, it is observed that the model obtained with generalized constitutive laws predicts better memory than the model obtained with artificial replacement. Further, these results are compared with the existing literature to verify the validity of the present results.

Suggested Citation

  • Muhammad Imran Asjad & Saif Ur Rehman & Ali Ahmadian & Soheil Salahshour & Mehdi Salimi, 2021. "First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1366-:d:574043
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    References listed on IDEAS

    as
    1. Qingkai Zhao & Hang Xu & Longbin Tao, 2017. "Unsteady Bioconvection Squeezing Flow in a Horizontal Channel with Chemical Reaction and Magnetic Field Effects," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, January.
    2. Zhang, Zizhen, 2020. "Corrigendum to a novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels [Chaos Solitons & Fractals 139 (2020) 110060]," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. M. R. Balooch Shahriyar & F. Ismail & S. Aghabeigi & A. Ahmadian & S. Salahshour, 2013. "An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, July.
    4. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Pakdaman, M. & Ahmadian, A. & Effati, S. & Salahshour, S. & Baleanu, D., 2017. "Solving differential equations of fractional order using an optimization technique based on training artificial neural network," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 81-95.
    6. Salahshour, S. & Ahmadian, A. & Abbasbandy, S. & Baleanu, D., 2018. "M-fractional derivative under interval uncertainty: Theory, properties and applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 84-93.
    7. Zhang, Zizhen, 2020. "A novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Tatiana Odzijewicz & Agnieszka B. Malinowska & Delfim F. M. Torres, 2012. "Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, May.
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    Cited by:

    1. Avramenko, A.A. & Kovetska, Yu.Yu. & Shevchuk, I.V., 2023. "Lorenz approach for analysis of bioconvection instability of gyrotactic motile microorganisms," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Abdul Manan & Saif Ur Rehman & Nageen Fatima & Muhammad Imran & Bagh Ali & Nehad Ali Shah & Jae Dong Chung, 2022. "Dynamics of Eyring–Powell Nanofluids When Bioconvection and Lorentz Forces Are Significant: The Case of a Slender Elastic Sheet of Variable Thickness with Porous Medium," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    3. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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