A variety of optical wave solutions to space–time fractional perturbed Kundu–Eckhaus model with full non-linearity

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu–Eckhaus model with full non-linearity are obtained by utilizing the \(\exp _a\) function technique and modified extended \(\tanh\) expansion function technique. The equation was independently introduced by Wiktor Eckhaus and by Anjan Kundu to model the propagation of waves in dispersive media. The model Kundu–Eckhaus equation is a general form of integrable system that is Gauge-equivalent to the mixed nonlinear Schrödinger equation. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The obtained solutions may be used for the propagation of the ultra-short femtosecond pulses and the rogue wave in an optical fiber. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.