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

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  • 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
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    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.
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    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.

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