This work provides an analytical investigation of the time-fractional Kundu–Eckhaus (KE) equation. We use the symmetry of the Lie group as an appropriate tool which deals with the wide class of fractional-order differential equations in Riemann–Liouville sense. In the current work, firstly, we employ classical Lie symmetries to obtain similarity reductions of nonlinear generalised time-fractional KE equation. At the final step, we find relevant exact solutions for the extracted generators.

中文翻译：

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非线性时间分数阶 Kundu-Eckhaus (KE) 方程的非经典李对称性和守恒定律

这项工作提供了时间分数 Kundu-Eckhaus (KE) 方程的分析研究。我们使用李群的对称性作为合适的工具来处理 Riemann-Liouville 意义上的各种分数阶微分方程。在目前的工作中，我们首先采用经典的李对称来获得非线性广义时间分数阶 KE 方程的相似度约简。在最后一步，我们为提取的生成器找到相关的精确解。