In this paper, the generalized exponential rational function method is used to construct exact solutions of the fl conformable-time RadhakrishnanKundu-Lakshmanan equation. This model governs soliton propagation dynamics through a polarization-preserving fiber. Fractional derivatives are described in the fl-conformable sense. As a result, we get new form of solitary traveling wave solutions for this model including novel soliton, traveling waves and kink-type solutions with complex structures. Physical interpretations of some extracted solutions are also included through taking suitable values of parameters and derivative order in them. It is proved that this method is powerful, efficient, and can be fruitfully implemented to establish new solutions of nonlinear conformable-time partial differential equations applied in mathematical physics.
