Solitary wave solutions and fractional effects of the time fractional equal width equation

In the present study, the \(\varrho\) -Laplace transform decomposition method ( \(\varrho\) -LTDM) is used to obtain approximate solutions of the time-fractional equal width equation (TFEWE). The proposed method combines the Adomian decomposition with the \(\varrho\) -Laplace transform. Fractional derivative treated in the Katugampola-Caputo sense. The considered model has important applications in several disciplines, including chemical physics, plasma physics, solid-state physics, fluid mechanics, and plasma wave propagation. The convergence and uniqueness of the proposed approach are also discussed. Moreover, graphical results for different fractional-order values and numerical simulations are presented to explain the behavior of the obtained solutions. From the results, it is evident that the proposed method is simple, accurate, and efficient. In addition, the method avoids rounding errors and does not require linearization, perturbation, discretization, or restrictive assumptions. Therefore, the suggested method can be extended to solve several kinds of nonlinear fractional partial differential equations (FPDEs).