New definition for traveling wave transformation and using of new con- formable fractional derivative for converting fractional nonlinear evolution equations into the ordinary differential equation are presented in this study. For this aim we consider the time and space fractional derivatives cubic nonlinear Schrodinger equa- tion. Then by using of the efficient and powerful method the exact traveling wave solutions of this equation are obtained. The new definition introduces a promising tool for solving many space-time fractional partial differential equations.
