AUTHOR=Wang Zhenli , Sun Liangji , Hua Rui , Su Lingde , Zhang Lihua 

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

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1133754

DOI=10.3389/fphy.2023.1133754

ISSN=2296-424X

ABSTRACT=<p>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 <italic>G</italic>′/<italic>G</italic>-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 <italic>G</italic>′/<italic>G</italic>-expansion approach is highly effective. Finally, conservation laws for the equation are well-built with a full derivation based on the Noether theorem.</p>