Abstract
In this paper, we constructed a traveling wave solutions expressed by three types of functions: hyperbolic, trigonometric, and rational. We used a fractional subequation method for some space-time fractional nonlinear partial differential equations (FNPDE), which are considered as models for different phenomena in natural and social sciences fields like engineering, physics, geology, etc. This method is very effective and easy to investigate exact traveling wave solutions to FNPDE with the aid of the modified Riemann-Liouville derivative.