A Comparative Study of the Fractional-Order Nonlinear System of Physical Models via Analytical Methods

Abstract

This article is related to the fractional-order analysis of one- and two-dimensional nonlinear systems of third-order KdV equations and coupled Burgers equations, applying modified analytical methods. The proposed problems will be solved with the Caputo–Fabrizio fractional derivative operator and the Yang transform. The results we obtained by implementing the suggested methods are compared with the exact solution. The convergence of the method is successfully presented and mathematically proved. To show the effectiveness of the proposed methods, we compared exact and analytical results with the help of graphs and tables, which are in strong agreement with each other. Also, the results obtained by implementing the suggested methods at various fractional orders are compared, confirming that solution gets closer to exact solution as the value tends from fractional order towards integer order. Moreover, the proposed methods are attractive, easy, and highly accurate, which confirms that these methods are suitable methods for solving partial differential equations or systems of partial differential equations.