  Recently, finding exact solutions of nonlinear fractional differential
equations has attracted great interest. In this paper, the space
time-fractional Klein-Gordon equation with cubic nonlinearities is examined.
Firstly, suitable exact soliton solutions are formally extacted by using the
solitary wave ansatz method. Some solutions are also illustrated by the
computer simulations. Besides, the modified Kudryashov method is used to
construct exact solutions of this equation.
