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Fractional modified Kawahara equation with Mittag–Leffler law

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  • Bhatter, Sanjay
  • Mathur, Amit
  • Kumar, Devendra
  • Nisar, Kottakkaran Sooppy
  • Singh, Jagdev

Abstract

In this work, we study a fractional extension of modified Kawahara equation by using Atangana–Baleanu fractional operator in the sense of Caputo (ABC). The fractional modified Kawahara equation is very useful to describe plasma waves and capillary-gravity water waves. We show existence and uniqueness of the solution of fractional modified Kawahara equation by making use of the fixed-point theorem. We obtain the solution of the fractional modified Kawahara equation with aid of the homotopy analysis transform technique. The outcomes of the investigation are demonstrated in graphical and tabular forms to show the influence of order of ABC fractional operator and variables on the displacement profile.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304606
    DOI: 10.1016/j.chaos.2019.109508
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Computational study of multi-species fractional reaction-diffusion system with ABC operator," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 280-289.
    3. Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2019. "A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    4. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    5. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
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    Cited by:

    1. 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.
    2. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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