The ${\varphi }^6$-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity

The ${\varphi }^6$-model expansion method combined with the conformable time-fractional derivative is applied in this paper for finding many new exact solutions including Jacobi elliptic function solutions, solitary wave solutions, trigonometric function solutions and other solutions to the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. This method presents a wider applicability for handling the nonlinear partial differential equations. Comparing our results with the well-known results are given.