The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

Abstract

In this paper, we consider the three‐dimensional non‐linear time‐fractional generalized Zakharov‐Kuznetsov (Z‐K) equation that describes the dust‐ion acoustic solitary waves in a magnetized dusty plasma. Based on the definition of the Riemann‐Liouville (R‐L) fractional derivatives, the analysis of the Lie group method can be applied to find the symmetries for the considered equation. After that, these symmetries enable us to transform the equation under study into a two‐dimensional non‐linear ordinary differential equation of fractional order in the sense of ErdLélyi‐Kober (E‐K) fractional operator. Also, we obtain a set of new analytical solutions for the time‐fractional generalized Z‐K equation via the power series and the fractional sub‐equation methods. Furthermore, we compute the conservation laws for this equation with a detailed derivation based on the formal Lagrangian.