SOLUTION OF FRACTIONAL MODIFIED KAWAHARA EQUATION: A SEMI-ANALYTIC APPROACH.

The present study introduces and explores the novel application of the Fractional Residual Power Series Method as a highly efficient and reliable approach for solving the challenging non-linear, time-fractional Kawahara and modified Kawahara equations. These equations, which are fifth-order, non-linear partial differential equations, are of significant importance in modeling shallow water waves. In contrast to existing methods such as the Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), and Adomian Decomposition Method (ADM), our research uniquely demon- strates the superior performance of the Fractional Residual Power Series Method. We emphasize that our approach not only outperforms these conventional techniques but also offers ease of implementation. This novel methodology promises to advance the field of mathematical modeling, providing a powerful tool for solving complex problems in the field of science and engineering. [ABSTRACT FROM AUTHOR]