The present article presents the technique for finding exact wave solutions of nonlinear fractional-order partial differential equations (NLFPDEs). The singular manifold method (SMM) is applied by starting with the fractional complex transformation (FCT) to reduce the equations to ordinary differential equations (ODEs). Then using the Bäcklund transformation (BT) and the resulting Schwarzian derivatives of the Eigen functions, a new variety of exact solutions is obtained. The method is applied to nonlinear (2 + 1) time-fractional Zoomeron equation, nonlinear (3 + 1) conformable time-fractional Zakharov–Kuznetsov equation, and nonlinear fractional Fokas equation. Some resulting solutions are graphically presented, revealing different solitary wave solutions.