In this paper, we investigate the time fractional system of fluid-conveying single-walled carbon nanotube (SWCNT), the generalization of SWCNT system which plays important roles in many applied fields. The corresponding Lie symmetries admitted by this fractional system in Riemann–Liouville sense are obtained and symmetry reductions are performed. In addition, based on the above symmetries, the conservation laws are derived using new Noether theorem. Furthermore, analytical solution and numerical series solution to the initial value problem of time fractional SWCNT system in Caputo sense are constructed by applying invariant subspace method and q-homotopy analysis method, respectively.

在本文中，我们研究了流体传输单壁碳纳米管（SWCNT）的时间分数系统，SWCNT系统的推广在许多应用领域中起着重要的作用。获得了该分数系统在黎曼-利维尔意义上承认的相应李对称性，并进行了对称约简。此外，基于上述对称性，使用新的Noether定理推导了守恒律。进一步，分别采用不变子空间法和q同伦分析法，构造了Caputo时间分数SWCNT系统初值问题的解析解和数值级数解。