Abstract
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.