This article concerns new analytical wave solutions of the Kuralay-II equations (K-IIAE
and K-IIBE) with exploration of a new definition of the derivative. This model is used in various
fields, like nonlinear optics, ferromagnetic materials and optical fibers. For this purpose, the expa
function, the extended sinh-Gordon equation expansion scheme, and the generalized Kudryashov
schemes were utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and
other kinds of solitons. These results are obtained and also verified by the Mathematica tool. Some
of the solutions are explained with 2-D, 3-D and contour plots using the Mathematica tool. The
solutions obtained succede the present solutions in the literature. For the first time, the effect of the
fractional derivative on the solutions is also shown graphically for this model. The analytical wave
solutions are highly desirable as they offer insights into the underlying physics or mathematics of a
system and provide a framework for further analysis. The results obtained can also be fruitful for the
development of models in the future. The schemes used in this research are effective, easy to apply,
and reliably handle other fractional non-linear partial differential equations.