The Analysis of Fractional-Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana-Baleanu fractional derivative operator are implemented to solve four systems. The obtained results by implementing the proposed methods are compared with exact solution. The convergence of the method is successfully presented and mathematically proved. The results we get are compared with exact solution through graphs and tables which confirms the effectiveness of the suggested techniques. In addition, the results obtained by employing the proposed approaches at different fractional orders are compared, confirming that as the value goes from fractional order to integer order, the result gets closer to the exact solution. Moreover, suggested techniques are interesting, easy, and highly accurate which confirm that these methods are suitable methods for solving any partial differential equations or systems of partial differential equations as well.

Automated summary

In this article, we solve nonlinear systems and coupled Burgers equations using two different methods and employing Laplace transform and Atangana-Baleanu fractional derivative operator. The convergence of the method is successfully demonstrated and mathematically proved by comparing the obtained results with exact solutions through graphs and tables. Moreover, the results obtained at different fractional orders are compared, confirming the suitability and effectiveness of the proposed techniques in solving partial differential equations or systems.