IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v178y2020icp407-421.html
   My bibliography  Save this article

On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas

Author

Listed:
  • Liu, Jian-Gen
  • Yang, Xiao-Jun
  • Feng, Yi-Ying
  • Cui, Ping

Abstract

In this article, the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov (Z–K) equation in quantum magneto-plasmas, is executed. First of all, the symmetry of this considered equation by using group analysis approach with the sense of Riemann–Liouville (R–L) fractional derivative, is obtained. Then, the symmetry of the above yielded, the optimal system of one-dimensional subalgebras for this equation is also found. Subsequently, the original equation can be reduced into (1+1)-dimensional fractional differential equation with the adding of extended Erdélyi–Kober fractional differential operator. Further, the one parameter group, invariant solutions and non-invariant solutions are constructed. Finally, the conservation laws are also shown with a new conservation theorem. We believe that these beautiful results can help us to discover more evolutionary mechanisms of the considered equation.

Suggested Citation

  • Liu, Jian-Gen & Yang, Xiao-Jun & Feng, Yi-Ying & Cui, Ping, 2020. "On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 407-421.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:407-421
    DOI: 10.1016/j.matcom.2020.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420302329
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.07.005?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. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    2. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
    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. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

    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. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Zehra Pinar Izgi & Pshtiwan Othman Mohammed & Ravi P. Agarwal & Majeed A. Yousif & Alina Alb Lupas & Mohamed Abdelwahed, 2024. "Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis," Mathematics, MDPI, vol. 12(18), pages 1-9, September.
    3. Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    5. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    6. Akbulut, Arzu & Taşcan, Filiz, 2017. "Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg–de Vries (mkdv) equation," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 1-6.
    7. Azadeh Naderifard & Elham Dastranj & S. Reza Hejazi, 2018. "Exact solutions for time-fractional Fokker–Planck–Kolmogorov equation of Geometric Brownian motion via Lie point symmetries," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-15, June.
    8. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
    9. Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.
    10. Gao, Ben & Zhang, Yao, 2019. "Symmetry analysis of the time fractional Gaudrey–Dodd–Gibbon equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1058-1062.
    11. Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    12. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Tianhang Gong & Wei Feng & Songlin Zhao, 2022. "Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation," Mathematics, MDPI, vol. 10(5), pages 1-21, February.

    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:178:y:2020:i:c:p:407-421. 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.