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Group classification of nonlinear time-fractional diffusion equation with a source term

Author

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  • Lukashchuk, S.Yu.
  • Makunin, A.V.

Abstract

A complete group classification is presented for a nonlinear time-fractional diffusion equation with a source term. The equation involves the Riemann–Liouville time-fractional derivative of the order α∈(0,2). All coefficients of the equation are sought as a function of the dependent variable. Using the infinitesimal approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration, and group classification is carried out up to the equivalence transformations. Examples of invariant solutions are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:335-343
    DOI: 10.1016/j.amc.2014.11.087
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    Cited by:

    1. 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).
    2. 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.

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