This work assigns to provide exact solutions for the time–fractional Coupled Equal Width Wave Equation (CEWE). We use the symmetry of the Lie group as an appropriate tool which deals with the wide class of fractional order differential equations in Riemann–Liouville sense. In the current work, firstly, we employ the classical Lie symmetries to obtain similarity reductions of nonlinear time-fractional CEWE equation. At the final step, we find the relevant exact solutions for the extracted generators. In summary based on the advantages of the obtained exact solutions, one can find this method a promising one to solve different nonlinear time–fractional equations.
