Numerical solutions and conservation laws of the time fractional coupled WBK‐type system

In this article, the general form of the fractional reduced differential transform method (FRDTM) to the (N + 1)‐dimensional cases was presented. Then, we applied the general FRDTM to handle the time fractional couple Whitham‐Broer‐Kaup's (WBK)‐type system. As a result, the numerical solution of this considered model was found. Next, based on the concepts of the nonlinear self‐adjointness and Noether operators, conservation laws for the time fractional coupled WBK‐type system was yielded. The results of the above obtained can help us better understand physics phenomena arising in describing propagation of shallow water waves.