Abstract In this article, the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov (Z–K) equation in quantum magneto-plasmas, is executed. First of all, the symmetry of this considered equation by using group analysis approach with the sense of Riemann–Liouville (R–L) fractional derivative, is obtained. Then, the symmetry of the above yielded, the optimal system of one-dimensional subalgebras for this equation is also found. Subsequently, the original equation can be reduced into (1+1)-dimensional fractional differential equation with the adding of extended Erdelyi–Kober fractional differential operator. Further, the one parameter group, invariant solutions and non-invariant solutions are constructed. Finally, the conservation laws are also shown with a new conservation theorem. We believe that these beautiful results can help us to discover more evolutionary mechanisms of the considered equation.

中文翻译：

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量子磁等离子体中时间分数扩展(2+1)维Zakharov-Kuznetsov方程的群分析

摘要 在本文中，执行了量子磁等离子体中时间分数扩展的 (2+1) 维 Zakharov-Kuznetsov (Z-K) 方程。首先，通过使用具有 Riemann-Liouville (R-L) 分数阶导数意义的群分析方法，获得了该方程的对称性。然后，根据上述产生的对称性，也找到了该方程的一维子代数的最优系统。随后，加入扩展的 Erdelyi-Kober 分数阶微分算子，将原方程简化为 (1+1) 维分数阶微分方程。进一步，构造了一个参数组，不变解和非不变解。最后，守恒定律也用新的守恒定理表示。