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Investigation of the fractional coupled viscous Burgers’ equation involving Mittag-Leffler kernel

Author

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  • Sulaiman, Tukur Abdulkadir
  • Yavuz, Mehmet
  • Bulut, Hasan
  • Baskonus, Haci Mehmet

Abstract

This study investigates the fractional coupled viscous Burgers’ equation under the Liouville–Caputo, Atangana–Baleanu and Yang–Srivastava–Machado fractional derivatives. With the help of fixed-point theorem, and using the Atangana–Baleanu fractional derivative with Mittag-Leffler kernel type kernel, we proved the existence and uniqueness of the studied model. The Laplace Homotopy perturbation method (LPM) defined with the Liouville–Caputo, Atangana–Baleanu and Yang–Srivastava–Machado operators is used in obtaining the exact solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed. We have seen the effect of the various parameters and variables on the displacement in Figs. 1–6.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:527:y:2019:i:c:s037843711930682x
    DOI: 10.1016/j.physa.2019.121126
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    Cited by:

    1. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Agahi, Hamzeh & Alipour, Mohsen, 2020. "Tsallis–Mittag-Leffler distribution and its applications in gas prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Akgül, Ali & Siddique, Imran, 2021. "Analysis of MHD Couette flow by fractal-fractional differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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