In this paper, exact traveling wave solutions of the conformable differential equations have been examined. By means of the wave transformation and properties of the conformable derivative (CD), conformable nonlinear Schro center dot dinger equation (CNLSE) has been converted into an integer order differential equation. To extract optical solutions, the wave profile has been divided into amplitude and phase components. A new extension of the Ba center dot cklund method has been offered and applied to the CNLSE which has important applications in quantum mechanics. Some novel exact traveling wave solutions to the CNLSE with group velocity dispersion and second order spatiotemporal dispersion coefficients are successfully obtained by means of this method.