The main objective of this research article is to summarize the study of the application of Lie symmetry reduction to the fractional-order coupled nonlinear complex Hirota system of partial differential equations. By the efficient use of symmetries and explicit solutions, this system reducing to nonlinear fractional ordinary differential equations (FODEs) with the application of Erdyli-Kober (E-K) operators for fractional derivatives and integrals depending on real order. Investigating the convergent series solution along with adjoint system and providing the conservation laws by Noether’s theorem.