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Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation

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  • Bakhshandeh-Chamazkoti, Rohollah
  • Alipour, Mohsen

Abstract

In this paper, the Lie symmetry analysis is proposed for a space–time convection–diffusion fractional differential equations with the Riemann–Liouville derivative by (2+1) independent variables and one dependent variable. We find a reduction form of our governed fractional differential equation using the similarity solution of our Lie symmetry. One-dimensional optimal system of Lie symmetry algebras is found. We present a computational method via the spectral method based on Bernstein’s operational matrices to solve the two-dimensional fractional heat equation with some initial conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:97-107
    DOI: 10.1016/j.matcom.2022.04.015
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    References listed on IDEAS

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    1. Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, June.
    2. 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.
    3. 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.
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