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An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense

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  • Hosseini, Kamyar
  • Ilie, Mousa
  • Mirzazadeh, Mohammad
  • Yusuf, Abdullahi
  • Sulaiman, Tukur Abdulkadir
  • Baleanu, Dumitru
  • Salahshour, Soheil

Abstract

The authors’ concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation.

Suggested Citation

  • Hosseini, Kamyar & Ilie, Mousa & Mirzazadeh, Mohammad & Yusuf, Abdullahi & Sulaiman, Tukur Abdulkadir & Baleanu, Dumitru & Salahshour, Soheil, 2021. "An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 248-260.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:248-260
    DOI: 10.1016/j.matcom.2021.02.021
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    References listed on IDEAS

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    1. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    4. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Nisar, Kottakkaran Sooppy & Singh, Jagdev, 2020. "Fractional modified Kawahara equation with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. Huang, Qiong-Ao & Zhang, Gengen & Wu, Bing, 2022. "Fully-discrete energy-preserving scheme for the space-fractional Klein–Gordon equation via Lagrange multiplier type scalar auxiliary variable approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 265-277.
    2. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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