Lie symmetry analysis, conservation laws and some exact solutions of the time-fractional Buckmaster equation

Abstract

This paper systematically investigates the Lie symmetry analysis of the time-fractional Buckmaster equation in the sense of Riemann–Liouville fractional derivative. With the aid of infinitesimal symmetries, this equation is transformed into a nonlinear ordinary differential equation of fractional order (FODE), where the fractional derivatives are in Erdelyi–Kober sense. The reduced FODE is solved with the explicit power series method and some figures for the obtained power series solutions are also depicted. Finally, Ibragimov’s method and Noether’s theorem have been employed to conclude the conservation laws of this equation.