In the present article, the local fractional derivatives and the exp(-Phi(xi))) method are used to construct the exact solutions of nonlinear space-time fractional partial differential equations. For illustrating the validity of the method, it is applied to the space-time fractional (3 + 1)-dimensional nonlinear Jimbo-Miwa equation and nonlinear Hirota-Satsuma coupled KdV system. This approach is an efficient mathematical tool for solving fractional differential equations and it can be applied to other nonlinear fractional differential equations. (C) 2016 Elsevier GmbH. All rights reserved.