Kink soliton phenomena of fractional conformable Kairat equations

This paper presents a new scientific method to obtain the precise soliton solutions of the fractional conformable Kairat-Ⅱ (K-IIE) and Kairat-X (K-XE) equations using the Riccati-Bernoulli sub-ODE technique and the Bäcklund transformation. These methods seem most effective compared to the previously used methods as they demonstrate novelty in intensity and potential application. The solutions attained in form of trigonometric, hyperbolic, and rational forms can be used in areas of nonlinear optics, ferromagnetic dynamics, photonic crystals, and optical fibers theory. The most important findings are displayed in simple $2D$ graphs in order to illustrate the nature of these solutions. The use of the flexible fractional derivatives shows that the models are integrated and provides opportunities for studying differential geometry and curve equivalence. Similarly, the ease of the methods underscores applications in other nonlinear partial differential equations, affirming their versatility and importance for the upper level courses.