In this work, we present ($G' /G, 1/G$)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems.The($G' /G, 1/G$)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.