In this study we focus on consideration of the nonlinear Wu-Zhang system with fractional derivative order. The system represents the propagation of dispersive long waves on shallow waters. By introducing conformable fractional transformation the nonlinear fractional partial differential equations are reduced  to nonlinear ordinary differential equations with integer order. We apply the Simple Equations Method (SEsM) for extracting exact analytical solutions of the reduced system. The solution of the system equations is constructed as a composite function of two functions including one independent variable. The two simpler functions are presented as finite series of the solutions of two simple equations. The simple equations used for this study are ordinary differential equations (ODEs) of first order, such as the ODE of Riccati and its particular variant, the ODE of Bernouli and the ODE of Abel of first kind. Numerical simulations of one of the obtained solutions are made to demonstrate the influence of the fractional derivative number and the traveling wave velocity on the profiles of the propagating traveling waves of the water elevation and the surface water velocity.