New analytical modelling of fractional generalized Kuramoto-Sivashinky equation via Atangana-Baleanu operator and J-transform method

In this paper, we propose a new analytical modelling of the well-known fractional generalized KuramotoSivashinky equation (FGKSE) using fractional operator with non-singular kernel and the homotopy analysis transform method via J -transform method. Also, using fixed-point theorem, we prove the existence and uniqueness of our proposed solution to the fractional Kuramoto-Sivashinky equation. To further validate the efficiency of the suggested technique, we proved the convergence analysis of the method and provide the error estimate. The obtained solutions of the FGKSE, describing turbulence processes in the field of ocean engineering are analytically and numerically compared to show the behaviors of many parameters of the present model. (c) 2022 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )