In this paper, we investigate the exact solutions and conservation laws of (2 + 1)-dimensional time fractional Navier–Stokes equations (TFNSE). Specifically, Lie symmetries and corresponding one-dimensional optimal system for TFNSE in Riemann–Liouville sense are obtained. Then, based on the admitted symmetries and optimal system, we reduce these equations to one-dimensional equations or (1 + 1)-dimensional fractional partial differential equations (PDEs) with the help of Erdélyi–Kober fractional differential operator and compound variable transformation. In addition, we solve the reduced PDEs applying power series expansion method and invariant subspace method, respectively. Furthermore, the conservation laws of TFNSE are derived using new Noether theorem.

在本文中，我们研究了 (2 + 1) 维时间分数 Navier-Stokes 方程 (TFNSE) 的精确解和守恒定律。具体而言，获得了黎曼-刘维尔意义上的 TFNSE 的李对称性和相应的一维最优系统。然后，基于公认的对称性和最优系统，我们借助 Erdélyi-Kober 分数阶微分算子和复合变量变换将这些方程简化为一维方程或 (1 + 1) 维分数阶偏微分方程 (PDE)。此外，我们分别应用幂级数展开法和不变子空间法求解约简偏微分方程。此外，TFNSE 的守恒定律是使用新的诺特定理推导出来的。