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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    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.

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