A comparative study of Lie symmetry analysis and invariant subspace methods to fractional Hunter-Saxton equation

Abstract

In this paper, a comparative study of the Lie group method and invariant subspace method is presented to derive the exact solution of the fractional Hunter-Saxton equation with the Riemann-Liouville fractional derivative. A systematic approach to finding the exact solution of the fractional Hunter-Saxton equation is illustrated using the Lie point symmetries as well as invariant subspaces. The optimal system of one-dimensional subalgebras of fractional Hunter-Saxton equations is derived. The Lie point symmetries transform given nonlinear fractional partial differential equation to a nonlinear ordinary differential equation of fractional order involving the similarity variable. The reduced ordinary differential equation involves Erdelyi-Kober fractional derivative. The obtained exact solutions are represented graphically and both methods are compared. The efficiency and computational feasibility of both methods are studied.