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Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics

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  • Mehmet Yavuz

    (Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Konya, Turkey
    Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Cornwall TR10 9FE, UK)

  • Ndolane Sene

    (Department of Mathematics, Institut des Politiques Publiques, Dakar Fann BP 5683, Senegal)

  • Mustafa Yıldız

    (Department of Mathematics, Faculty of Arts and Sciences, Bülent Ecevit University, Incivez, 67100 Zonguldak, Turkey)

Abstract

This work proposes a qualitative study for the fractional second-grade fluid described by a fractional operator. The classical Caputo fractional operator is used in the investigations. The exact analytical solutions of the constructed problems for the proposed model are determined by using the Laplace transform method, which particularly includes the Laplace transform of the Caputo derivative. The impact of the used fractional operator is presented; especially, the acceleration effect is noticed in the paper. The parameters’ influences are focused on the dynamics such as the Prandtl number ( P r ) , the Grashof numbers ( G r ) , and the parameter η when the fractional-order derivative is used in modeling the second-grade fluid model. Their impacts are also analyzed from a physical point of view besides mathematical calculations. The impact of the fractional parameter α is also provided. Finally, it is concluded that the graphical representations support the theoretical observations of the paper.

Suggested Citation

  • Mehmet Yavuz & Ndolane Sene & Mustafa Yıldız, 2022. "Analysis of the Influences of Parameters in the Fractional Second-Grade Fluid Dynamics," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1125-:d:785026
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Jajarmi, Amin & Yusuf, Abdullahi & Baleanu, Dumitru & Inc, Mustafa, 2020. "A new fractional HRSV model and its optimal control: A non-singular operator approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Ndolane Sene, 2021. "A Numerical Algorithm Applied to Free Convection Flows of the Casson Fluid along with Heat and Mass Transfer Described by the Caputo Derivative," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-11, June.
    4. Saqib, Muhammad & Khan, Ilyas & Shafie, Sharidan, 2018. "Application of Atangana–Baleanu fractional derivative to MHD channel flow of CMC-based-CNT's nanofluid through a porous medium," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 79-85.
    5. Atangana, Abdon & Mekkaoui, Toufik, 2019. "Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 366-381.
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    Cited by:

    1. Ndolane Sene, 2023. "Solution Procedure for Fractional Casson Fluid Model Considered with Heat Generation and Chemical Reaction," Sustainability, MDPI, vol. 15(6), pages 1-19, March.
    2. Wenchang He & Yuhang Jin & Luyao Wang & Ning Cai & Jia Mu, 2024. "Existence and Stability for Fractional Differential Equations with a ψ –Hilfer Fractional Derivative in the Caputo Sense," Mathematics, MDPI, vol. 12(20), pages 1-12, October.

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