Novel Analysis of Fractional-Order Fifth-Order Korteweg-de Vries Equations

In this paper, the rho-homotopy perturbation transformation method was applied to analysis of fifth-order nonlinear fractional Korteweg-de Vries (KdV) equations. This technique is the mixture form of the rho-Laplace transformation with the homotopy perturbation method. The purpose of this study is to demonstrate the validity and efficiency of this method. Furthermore, it is demonstrated that the fractional and integer-order solutions close in on the exact result. The suggested technique was effectively utilized and was accurate and simple to use for a number of related engineering and science models.

Automated summary

In this study, the rho-homotopy perturbation transformation method was applied to analyze fifth-order nonlinear fractional KdV equations, demonstrating its validity and efficiency, as well as showing that the solutions for fractional and integer orders converge to the exact results. The technique was successfully utilized for various engineering and science models, proving to be accurate and easy to use.