In this paper, the Lie symmetry analysis was executed for the nonlinear fractional-order conduction-diffusion Buckmaster model (BM), which involves the Riemann-Liouville (R-L) derivative of fractional-order 'β'. In the study of groundwater flow and oil reservoir engineering where fluid flow through porous materials is crucial, BM played an important role. The Lie point infinitesimal generators and Lie algebra were constructed for the equation. The Lie symmetries were acquired for the ordinary fractional-order BM. The power series solution and its convergence were also analyzed with the application of the implicit theorem. Noether's theorem was employed to ensure the consistency of a system by deriving the conservation laws of its physical model.