Modeling and Dynamical Analysis of Time‐Fractional Nonlinear Dispersive Models Under Nonsingular Kernel Operators

It is highly challenging to examine solutions to fractional differential equations. Mathematicians face various challenges, especially when trying to solve fractional partial differential equations. There are now a lot of models in fractional calculus that need to be developed, investigated, and applied in real‐world situations in various scientific fields where nonlocality is crucial. Numerous nonlocal phenomena have not been researched and are simply waiting to be explored, despite the fact that many amazing discoveries have already been presented by researchers in significant monographs and review articles. As a result, we are always learning about novel aspects and applications of fractional models. In this work, we analyze the time‐fractional nonlinear dispersive K(m,n,1) type equations employing the natural transform decomposition approach. We explore the nonsingular kernel derivatives, the Caputo–Fabrizio and Atangana–Baleanu in the Caputo sense. Numerical and graphical comparisons are made between the obtained results and the exact solutions. The numerical simulations are provided to ensure the efficacy of the technique being studied. The present method clearly shows the behavior of the findings for different fractional orders. It is found that the results obtained closely resemble the actual results of the problems stated. Also, we compare our findings with those of the Mohand transform iterative method (MTIM). The outcomes show that the present method is reliable, strong, and efficient. The approach given can be used to solve a wide range of partial fractional differential equations.