Classical and non-classical Lie symmetry analysis, conservation laws and exact solutions of the time-fractional Chen–Lee–Liu equation

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. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.