Numerous Exact Solutions of the Wu-Zhang System with Conformable Time–Fractional Derivatives via Simple Equations Method (SEsM): The Case of Two Simple Equations

In this study we consider the nonlinear Wu-Zhang system with fractional derivative order. The system describes the propagation of dispersive long waves on shallow waters. By an appropriate transformation we reduce the nonlinear fractional partial differential equations to nonlinear ordinary differential equations with integer order. We apply the Simple Equations Method (SEsM) for obtaining exact analytical solutions of the reduced system. We present the general solution of the system equations by composite functions of two simpler functions which are power series of solutions of two simple equations. We choose the simple equations used for this study to be ordinary differential equations of second order. Depending on numerical values of the coefficients of the simple equations, numerous particular solutions of the studied system are obtained. Several numerical examples of the obtained solutions are presented.