lie symmetries, conservation laws, optimal system and power series solutions of (3+1)-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.