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

2022/04/17 by Rohollah Bakhshandeh‐Chamazkoti, Bakhshandeh-Chamazkoti, Rohollah, Mohsen Alipour +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2204.08028

openalex publication_date 2022/04/17 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

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.

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