An efficient computational technique for time-fractional Kaup-Kupershmidt equation

In this article, an efficient novel technique, namely the q-homotopy analysis transform method (q-HATM) is applied to find the solution for the time-fractional Kaup-Kupershmidt (KK) equation. The KK equation plays a vital role while studying the capillary gravity waves and nonlinear dispersive waves. To check the effectiveness and pertinency of the projected method, we consider three distinct cases of the fractional nonlinear KK equation. The q-HATM provides the auxiliary parameter PLANCK CONSTANT OVER TWO PI, called convergence control parameter, with the help of that we can manipulate and adjust the area of convergence of the series solution. Moreover, to authenticate the accuracy and reliability of the considered technique the numerical simulations have been presented. The retrieved results ensure that the projected scheme is effortless to carry out and analyze the highly nonlinear problems arising in science and technology.

Automated summary

The study applied the q-homotopy analysis transform method to solve the time-fractional Kaup-Kupershmidt equation and verified its accuracy and reliability through numerical simulations, demonstrating its strong applicability for handling highly nonlinear problems.