Abstract
The analytical solution of fractional-order regularized long waves in the context of various operators is presented in this study as a framework for the homotopy perturbation transform technique. To investigate regularized long wave equations, we first establish the Yang transform of the fractional Caputo and Caputo-Fabrizio operators. The fractional order regularized long wave equation is solved using the Yang transform as well. The accuracy of the proposed operators are verified using numerical problems, and the resulting solutions are shown in the figures. The solutions demonstrate how the suggested approach is accurate and suitable for analyzing nonlinear physical and engineering challenges.