Solving the Space -Time Fractional RLW and MRLW Equations Using Modified Extended Tanh Method with the Riccati Equation

In the present paper, a traveling wave solution has been established using the modified extended tanh method for space-time fractional nonlinear partial differential equations. We used this method to find exact solutions for different types of the space-time fractional nonlinear partial differential equations such as space-time fractional regularized long wave equation (RLWE) and space-time fractional modified regularized long wave equation (MRLW) which are the important soliton equations. Both equations are reduced to ordinary differential equations by using of fractional complex transform and properties of modified Riemann-Liouville derivative.