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Analysis of MHD Couette flow by fractal-fractional differential operators

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  • Akgül, Ali
  • Siddique, Imran

Abstract

In this paper, an analysis is carried out to study the MHD Couette flow (flow between two parallel plates such that the upper plate is moving with constant velocity while the lower plate is at rest) for an incompressible viscous fluid under isothermal conditions. The governing equations are developed from the problem, formulated with the recently presented fractal-fractional operators in Riemann–Liouville sense with power law, exponential decay and the Mittag–Leffler law kernels. For each operator, we present a comprehensive analysis including, the numerical solutions, stability analysis and error analysis. We apply very accurate method to get the desired results. We demonstrate the numerical simulations to prove the efficiency of the proposed method.

Suggested Citation

  • Akgül, Ali & Siddique, Imran, 2021. "Analysis of MHD Couette flow by fractal-fractional differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002460
    DOI: 10.1016/j.chaos.2021.110893
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    References listed on IDEAS

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    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    3. Atangana, Abdon, 2020. "Fractional discretization: The African’s tortoise walk," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Siddique, Imran & Akgül, Ali, 2020. "Analysis of MHD generalized first problem of Stokes’ in view of local and non-local fractal fractional differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Sulaiman, Tukur Abdulkadir & Yavuz, Mehmet & Bulut, Hasan & Baskonus, Haci Mehmet, 2019. "Investigation of the fractional coupled viscous Burgers’ equation involving Mittag-Leffler kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    6. Atangana, Abdon & Khan, Muhammad Altaf, 2019. "Validity of fractal derivative to capturing chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 50-59.
    7. Atangana, Abdon & Shafiq, Anum, 2019. "Differential and integral operators with constant fractional order and variable fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 226-243.
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