IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v391y2021ics0096300320306068.html
   My bibliography  Save this article

Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation

Author

Listed:
  • Hejazi, S. Reza
  • Saberi, Elaheh
  • Mohammadizadeh, Fatemeh

Abstract

The non-linear anomalous diffusion in anisotropic media is using in various fields, e.g. in molecular dynamics, hydrology, financial systems, porous media analysis, etc. The Lie group method is developed to study the time-fractional diffusion equation with a source term in anisotropic media. As an application, the complete Lie group classification is performed up to the equivalence transformations for all special cases of the coefficients. Some similarity reductions are obtained for implicit cases. The analytical invariant subspace method is used in order to find some exact solutions. The work is concluded by the fractional Chebyshev pseudo-spectral (FCPS) method for constructing a numerical simulation for some of the reduced equations in the symmetry analysis section.

Suggested Citation

  • Hejazi, S. Reza & Saberi, Elaheh & Mohammadizadeh, Fatemeh, 2021. "Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320306068
    DOI: 10.1016/j.amc.2020.125652
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320306068
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125652?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. Guan, Xue & Liu, Wenjun & Zhou, Qin & Biswas, Anjan, 2020. "Some lump solutions for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    3. Liu, Wenjun & Zhang, Yujia & Wazwaz, Abdul Majid & Zhou, Qin, 2019. "Analytic study on triple-S, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 325-331.
    4. Lukashchuk, S.Yu. & Makunin, A.V., 2015. "Group classification of nonlinear time-fractional diffusion equation with a source term," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 335-343.
    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. Mohammadizadeh, Fatemeh & Rashidi, Saeede & Hejazi, S. Reza, 2021. "Space–time fractional Klein-Gordon equation: Symmetry analysis, conservation laws and numerical approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 476-497.

    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. Ochoa-Tapia, J. Alberto & Valdes-Parada, Francisco J. & Alvarez-Ramirez, Jose, 2007. "A fractional-order Darcy's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 1-14.
    2. Owolabi, Kolade M., 2016. "Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 89-98.
    3. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
    4. Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Veni, S. Saravana & Rajan, M.S. Mani, 2021. "Attosecond soliton switching through the interactions of two and three solitons in an inhomogeneous fiber," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Wang, Yiduan & Zheng, Shenzhou & Zhang, Wei & Wang, Guochao & Wang, Jun, 2018. "Fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 486-498.
    7. Bolster, Diogo & Benson, David A. & Meerschaert, Mark M. & Baeumer, Boris, 2013. "Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2513-2525.
    8. Islam Samir & Ahmed H. Arnous & Yakup Yıldırım & Anjan Biswas & Luminita Moraru & Simona Moldovanu, 2022. "Optical Solitons with Cubic-Quintic-Septic-Nonic Nonlinearities and Quadrupled Power-Law Nonlinearity: An Observation," Mathematics, MDPI, vol. 10(21), pages 1-9, November.
    9. Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    10. Vasily E. Tarasov, 2021. "General Fractional Vector Calculus," Mathematics, MDPI, vol. 9(21), pages 1-87, November.
    11. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.
    12. Rizvi, Syed Tahir Raza & Khan, Salah Ud-Din & Hassan, Mohsan & Fatima, Ishrat & Khan, Shahab Ud-Din, 2021. "Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 126-136.
    13. Troparevsky, M.I. & Muszkats, J.P. & Seminara, S.A. & Zitto, M.E. & Piotrkowski, R., 2022. "Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    14. Prodanov, Dimiter, 2016. "Characterization of strongly non-linear and singular functions by scale space analysis," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 14-19.
    15. Zhang, Run-Fa & Li, Ming-Chu & Albishari, Mohammed & Zheng, Fu-Chang & Lan, Zhong-Zhou, 2021. "Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    16. Bakhshandeh-Chamazkoti, Rohollah & Alipour, Mohsen, 2022. "Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 97-107.

    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:apmaco:v:391:y:2021:i:c:s0096300320306068. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.