Lie symmetry analysis, invariant subspace method and q-homotopy analysis method for solving fractional system of single-walled carbon nanotube

Abstract

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.