IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p687-d756329.html
   My bibliography  Save this article

Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation

Author

Listed:
  • Tianhang Gong

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Wei Feng

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

  • Songlin Zhao

    (Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China)

Abstract

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point symmetry groups and the corresponding optimal subgroups are determined. Then, the similarity reduction is performed to the given equation and some explicit solutions are derived. The asymptotic behaviours for the solutions are also discussed. Through the concept of nonlinear self-adjointness, the conservation laws arising from the admitted point symmetries are listed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:687-:d:756329
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/687/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/687/
    Download Restriction: no
    ---><---

    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. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
    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. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.

    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. 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).
    2. 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.
    3. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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 & 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.
    12. 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.
    13. Habibi, Noora & Lashkarian, Elham & Dastranj, Elham & Hejazi, S. Reza, 2019. "Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker–Planck equations for special stochastic process in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 750-766.

    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:gam:jmathe:v:10:y:2022:i:5:p:687-:d:756329. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.