  Integral form of the space-time-fractional Schr\"odinger equation for the
scattering problem in the fractional quantum mechanics is studied in this
paper. We define the fractional Green's function for the space-time fractional
Schrodinger equation and express it in terms of Fox's H-function and in a
computable series form. The asymptotic formula of the Green's function for
large argument is also obtained, and applied to study the fractional quantum
scattering problem. We get the approximate scattering wave function with
correction of every order.
