LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Jicheng Yu; Yuqiang Feng

doi:10.11948/20220268

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 1872-1889

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Jicheng Yu, Yuqiang Feng. LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1872-1889. doi: 10.11948/20220268

Citation:

Jicheng Yu, Yuqiang Feng. LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1872-1889. doi: 10.11948/20220268

LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Jicheng Yu^1,,
Yuqiang Feng^2, ,

1.
School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China
2.
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, Hubei, China

Author Bio: Email: yjicheng@126.com(J. Yu)
Corresponding author: Email: yqfeng6@126.com(Y. Feng)
Fund Project: The authors were supported by the State Key Program of National Natural Science Foundation of China (No. 72031009)

Abstract

Abstract

In this paper, Lie symmetry analysis method is applied to space-time fractional reaction-diffusion equations and diffusion-convection Boussinesq equations. The Lie symmetries for the governing equations are obtained and used to get group generators for reducing the space-time fractional partial differential equations(FPDEs) with Riemann-Liouville fractional derivative to space-time fractional ordinary differential equations(FODEs) with Erdélyi-Kober fractional derivative. Then the Laplace transformation and the power series methods are applied to derive explicit solutions for the reduced equations. Moreover, the conservation theorems and the generalization of the Noether operators are developed to acquire the conservation laws for the equations. Some figures for the obtained explicit solutions are also presented.
- Lie symmetry analysis /
- space-time fractional differential equation /
- Riemann-Liouville fractional derivative /
- Erddélyi-Kober fractional derivative /
- exact solution /
- conservation law
MSC: 35B06, 47F05, 35K57, 26A33

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