IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp62-76.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304699
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.12.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ariza-Hernandez, Francisco J. & Martin-Alvarez, Luis M. & Arciga-Alejandre, Martin P. & Sanchez-Ortiz, Jorge, 2021. "Bayesian inversion for a fractional Lotka-Volterra model: An application of Canadian lynx vs. snowshoe hares," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Attia, Nourhane & Akgül, Ali & Seba, Djamila & Nour, Abdelkader, 2020. "An efficient numerical technique for a biological population model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Izadi, Mohammad & Yüzbaşı, Şuayip & Adel, Waleed, 2022. "Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    5. Defterli, Ozlem, 2021. "Comparative analysis of fractional order dengue model with temperature effect via singular and non-singular operators," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. McAllister, A. & McCartney, M. & Glass, D.H., 2023. "Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    7. Abu Arqub, Omar & Al-Smadi, Mohammed, 2020. "An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
    9. Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    10. Jaradat, I. & Al-Dolat, M. & Al-Zoubi, K. & Alquran, M., 2018. "Theory and applications of a more general form for fractional power series expansion," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 107-110.
    11. Mohamed Elbadri & Mohamed A. Abdoon & Mohammed Berir & Dalal Khalid Almutairi, 2023. "A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods," Mathematics, MDPI, vol. 11(13), pages 1-11, July.
    12. H. Mesgarani & Y. Esmaeelzade Aghdam & A. Beiranvand & J. F. Gómez-Aguilar, 2024. "A Novel Approach to Fuzzy Based Efficiency Assessment of a Financial System," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1609-1626, April.
    13. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Shadimetov, Kh.M. & Hayotov, A.R. & Nuraliev, F.A., 2016. "Optimal quadrature formulas of Euler–Maclaurin type," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 340-355.
    15. Mohammed Shqair & Ahmad El-Ajou & Mazen Nairat, 2019. "Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    16. Cecilia Berardo & Iulia Martina Bulai & Ezio Venturino, 2021. "Interactions Obtained from Basic Mechanistic Principles: Prey Herds and Predators," Mathematics, MDPI, vol. 9(20), pages 1-18, October.
    17. Matouk, A.E. & Lahcene, Bachioua, 2023. "Chaotic dynamics in some fractional predator–prey models via a new Caputo operator based on the generalised Gamma function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    18. Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    19. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    20. Feng, Yi-Ying & Yang, Xiao-Jun & Liu, Jian-Gen & Chen, Zhan-Qing, 2023. "Mechanical investigations of local fractional magnetorheological elastomers model on Cantor sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:62-76. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.