Time-fractional generalized fifth-order KdV equation: Lie symmetry analysis and conservation laws

The purpose of this study is to apply the Lie group analysis method to the time-fractional order generalized fifth-order KdV (TFF-KdV) equation. We examine applying symmetry analysis to the TFF-KdV equation with the Riemann–Liouville (R–L) derivative, employing the G ′/ G -expansion approach to yiel...

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Bibliographic Details
Published in:Frontiers in physics 2023-03, Vol.11
Main Authors: Wang, Zhenli, Sun, Liangji, Hua, Rui, Su, Lingde, Zhang, Lihua
Format: Article
Language:English
Subjects:
conservation laws
G′/G-expansion method
Lie group analysis
Riemann–Liouville derivative
time-fractional generalized fifth-order KdV (TFF-KdV) equation
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Summary:The purpose of this study is to apply the Lie group analysis method to the time-fractional order generalized fifth-order KdV (TFF-KdV) equation. We examine applying symmetry analysis to the TFF-KdV equation with the Riemann–Liouville (R–L) derivative, employing the G ′/ G -expansion approach to yield trigonometric, hyperbolic, and rational function solutions with arbitrary constants. The discovered solutions are unique and have never been studied previously. For solving non-linear fractional partial differential equations, we find that the G ′/ G -expansion approach is highly effective. Finally, conservation laws for the equation are well-built with a full derivation based on the Noether theorem.
ISSN:2296-424X
2296-424X
DOI:10.3389/fphy.2023.1133754