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=Volume 11 - 2023

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=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 examined 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 seen before. For solving nonlinear fractional partial differential equations, 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.