SOLVING NONLINEAR TIME-FRACTIONAL KAWAHARA AND MODIFIED KAWAHARA EQUATIONS USING THE LAPLACE RESIDUAL POWER SERIES METHOD

Abstract

In this study, we efficiently obtain numerical solutions for the nonlinear timefractional Kawahara and modified Kawahara equations using the Laplace residual power series method (L-RPSM), which combines the Laplace transform with the residual power series approach. We demonstrate the procedure, validity, and applicability of the proposed method by solving both equations with arbitrary initial conditions. To validate the theoretical results, we apply three distinct test problems. The results are presented in tabular form and visually represented in both two- and three-dimensional graphs, showing that the solutions converge to the exact results. Additionally, the results highlight the impact of the time-Caputo fractional operator on the obtained solutions and demonstrate that the proposed method offers more accurate approximations compared to other methods, such as the Adomian decomposition method (ADM), the variational iteration method (VIM), the residual power series method (RPSM), and the homotopy perturbation method (HPM).