The analysis of the fractional-order system of third-order KdV equation within different operators

This paper studies the fractional system of the third-order Korteweg-De Vries equation under the fractional derivatives of Caputo, Atangana-Baleanu and Yang-Srivastava-Machado. The Homotopy perturbation transform technique defined with the Caputo, Atangana-Baleanu and Yang-Srivastava-Machado operators is applied to achieve the non-linear model’s actual results. This non-linear scheme generally arises as a description of waves in traffic flow, electric circuits, elastic media and electrodynamics, multi-component plasmas, shallow water waves etc. This research aims to develop a new class of methods that do not require small parameters to find approximate solutions of fractional coupled systems and eliminate unrealistically and linearization factors. Analytical simulation demonstrates that the suggested method is reliable, efficient, and straightforward to various physical systems. This study demonstrates that Homotopy perturbation transform method numerical solutions are very accurate and effective for analyzing the non-linear behavior of a system. According to the research, the Homotopy perturbation transform method is much easier, more convenient, and more efficient than other analytical techniques.