In this paper, the (G'/G)-expansion method is presented for finding the exact solutions of the space-time fractional traveling wave solutions for the Joseph-Egri (TRLW) equation and Gardner equation. The fractional derivatives are described by modified Riemann-Liouville sense. Many exact solutions are obtained by the hyperbolic functions, the trigonometric functions and the rational functions. This method is efficient and powerful in performing a solution to the fractional partial differential equations. Also, the method reduces the large amount of calculations.