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Stokes’ first problem for heated flat plate with Atangana–Baleanu fractional derivative

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  • Sene, Ndolane

Abstract

In this paper, we investigate on the exact solutions of the Stokes’ first problem for generalized second grade fluid with a new fractional derivative operator. The Riemann–Liouville and the Caputo fractional derivative are substituted by the Atangana–Baleanu fractional derivative in the Stokes’ first fractional differential equation. With the Laplace transform given by the Atangana–Baleanu fractional derivative operator, we give for the Stokes’ first fractional differential equations the exact solutions for the velocity and temperature field. The Fourier sine transform and the Laplace transform will be used to get the exact solutions of the Stokes’ first fractional differential equations. The solutions of the Stokes’ first differential equations for a viscous Newtonian fluid, as well as those corresponding to a second grade fluid, are obtained in limiting cases, and an approach with the graphical surfaces representations for the exact solutions is proposed.

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  • Sene, Ndolane, 2018. "Stokes’ first problem for heated flat plate with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 68-75.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:68-75
    DOI: 10.1016/j.chaos.2018.10.014
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
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    Cited by:

    1. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Fall, Aliou Niang & Ndiaye, Seydou Nourou & Sene, Ndolane, 2019. "Black–Scholes option pricing equations described by the Caputo generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 108-118.
    4. Mansal, Fulgence & Sene, Ndolane, 2020. "Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Sene, Ndolane, 2020. "Second-grade fluid model with Caputo–Liouville generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Sene, Ndolane & Abdelmalek, Karima, 2019. "Analysis of the fractional diffusion equations described by Atangana-Baleanu-Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 158-164.

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