Abstract
In this article, our focus is to extract the diverse exact solutions to the conformable time-fractional modified nonlinear Schrödinger equation (CTFMNLSE) that describes the propagation of water waves in the ocean engineering. Diverse exact solutions like trigonometric, hyperbolic and exponential function solutions are extracted. We also secure some other special wave solutions in the forms of shock wave, singular, multiple and mixed complex solitons. The generalized exponential rational function method (GERFM) is used to explain the dynamics of soliton to CTFMNLSE. Furthermore, the constraint conditions for the existence of solutions are reported also singular periodic wave solutions are recovered. Besides, the accomplished solutions are beneficial to interpretation of the wave propagation study and also important for numerical and experimental verifications in ocean engineering
•The Soliton solutions and Conformable fractional derivative.•The MNLSE and GERFM dynamical equation are considered.•Dispersive of propagation wave structures are obtained.•We applied hydrodynamic mathematical methods.