Lie symmetries, conservation laws, optimal system and power series solutions of (۳+۱)-dimensional fractional Zakharov-Kuznetsov equation

In this paper, the Lie symmetry analysis method is applied to the high dimensional fractional Zakharov-Kuznetsov equation. All Lie symmetries and the corresponding conserved vectors for the equation are obtained. The one-dimensional optimal system is utilized to reduce the aimed equation with Riemann-Liouville fractional derivative to a low-dimensional fractional partial differential equation with Erdelyi-Kober fractional derivative. Then the power series solution of the reduced equation is given. Moreover, some other low dimensional reduced fractional differential equations with Riemann-Liouville fractional derivatives are obtained and can be solved by different methods in the literatures herein.

Keywords:

Lie symmetry analysis , fractional Zakharov-Kuznetsov equation , Conservation laws , one-dimensional optimal system , power series solution