Solitons and travelling waves structure for M-fractional Kairat-II equation using three explicit methods

Abstract Exact solutions of (1+1)-dimensional M-fractional Kairat-II equation are obtained via proposed three extended mathematical methods with the help of the computational software Mathematica. This model has many applications in optical fibers, which is used to describe the trajectory of optical pulses in optical fibers. The derived solutions are novel and newer existing in any kind of literature. The constructed solutions are in distinct form, such as trigonometric, hyperbolic, exponential, and rational functions. For the physical phenomena of concern fractional model, some obtained solutions are plotted in two-dimensional and three-dimensional by assigning the specific values to the parameters under the constrain conditions. Moreover, the proposed methods are enormously superbly mathematical tools to review wave solutions of several fractional models in nonlinear science.