Structures of exact solutions for the modified nonlinear Schrödinger equation in the sense of conformable fractional derivative

This paper is devoted to discuss analytically the conformable time-fractional modified nonlinear Schrödinger equation with the aid of efficient methods. The suggested model is a model used in ocean engineering to explain the propagation of water waves. At this stage, while using the proposed methods, the first step is to reduce the model defined by the conformable fractional derivative to the ordinary differential equation system with an appropriate transformation. We have obtained a variety of new families of exact traveling wave solutions including trigonometric, hyperbolic and exponential types. In related subject, the Adomian decomposition method is implemented to approximate the one of the solution of the underlying equation. For dynamic properties of the obtained solutions, we have depicted them graphically using computer programming to explain more efficiently the behavior of different shapes of solutions for the different values of free parameters with constraint conditions. Finally, a comparison is given for the solutions obtained in this study.