In this paper, we studied a higher-dimensional space and time fractional model, namely, the (3+1)-dimensional dissipative Burgers equation which can be used to describe the shallow water waves phenomena. Here, the analyzed tool is the Lie symmetry scheme in the sense of the Riemann–Liouville fractional derivative. First of all, the symmetry of this considered equation was yielded. Then, based on the above obtained symmetry, the one-parameter Lie group was obtained. Subsequently, this model can be changed into the lower-dimensional equation with the Erdélyi–Kober fractional operators. Lastly, conservation laws of this studied equation via a new conservation theorem were also received. After such a series of processing, these new results play an important role in our understanding of this higher-dimensional space and time differential equations.

在本文中，我们研究了一个更高维的时空分数模型，即（3+1）维耗散Burgers方程，它可以用来描述浅水波浪现象。在这里，分析的工具是黎曼-刘维尔分数导数意义上的李对称方案。首先，产生了这个考虑的方程的对称性。然后，基于上述得到的对称性，得到一参数李群。随后，这个模型可以用 Erdélyi-Kober 分数算子转化为低维方程。最后，还通过新的守恒定理得到了这个研究方程​​的守恒定律。经过这样一系列的处理，这些新的结果对我们理解这个更高维的时空微分方程起到了重要的作用。