This paper presents an approach for solving fractional differential equations by employing the exp-function method and (G'/G)-expansion method. These methods were applied in two examples to solve non-linear fractional differential equations. The fractional derivatives are described in the modified Riemann-Liouville sense. As a result, many exact analytical solutions are obtained including hyperbolic function solutions and trigonometric function solutions. The results also show that the methods are very effective and convenient for solving nonlinear partial differential equations of fractional order.