The current work deals with the classical and non-classical Lie group analysis for the fractional
type system of nonlinear Chen–Lee–Liu (CLL) equations. The invariance surface
condition is imposed to this system of fractional differential equations to find non-classical
generators. Non-classical and classical Lie symmetry analysis are used to similarity reductions
of this system. Corresponding exact solutions are obtained for the extracted generators
in both classical and non-classical senses. Convergence of the obtained solutions when fractional
order tends to the integer one, is graphically checked. Finally, the conservation laws are
investigated for the system of time-fractional CLL equations, specially for the non-classical
vector fields.