The modified extended tanh method with the Riccati equation for solving the space-time fractional EW and MEW equations

In this paper, we established a traveling wave solution by using the modified extended tanh method for space-time fractional nonlinear partial differential equations. The method is used to obtain exact solutions for different types of space-time fractional nonlinear partial differential equations such as space-time fractional equal width wave equation (EWE) and space-time fractional modified equal width wave equation (MEW) which are important soliton equations. Both equations are reduced to ordinary differential equations by using fractional complex transform and properties of modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.