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Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation

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  • Alquran, Marwan
  • Yousef, Feras
  • Alquran, Farah
  • Sulaiman, Tukur A.
  • Yusuf, Abdullahi

Abstract

In this paper, the conformable-time-fractional Klein–Fock–Gordon equation is considered and solved using the Kudryashov-expansion method to extract dual-wave solutions. Only, the quadratic and the cubic cases of the model are investigated. It has been noticed that physical changes in the construction of the obtained solutions are reported in the case of transition from the quadratic-state into the cubic-state. Additionally, the Caputo-time-fractional quadratic–cubic Klein–Fock–Gordon is also considered and studied by implementing the residual power series method. A comparison between these two types of fractional derivatives is discussed and the 2D–3D plots are provided to support the findings of this work.

Suggested Citation

  • Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:62-76
    DOI: 10.1016/j.matcom.2020.12.014
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    1. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    3. Alquran, Marwan & Jaradat, Imad, 2019. "Delay-asymptotic solutions for the time-fractional delay-type wave equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
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    Cited by:

    1. Khirsariya, Sagar R. & Chauhan, Jignesh P. & Rao, Snehal B., 2024. "A robust computational analysis of residual power series involving general transform to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 168-186.
    2. Qi, Jianming & Li, Xinwei & Bai, Leiqiang & Sun, Yiqun, 2023. "The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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