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Integral form of the space-time-fractional Schr\"odinger equation for thescattering problem in the fractional quantum mechanics is studied in thispaper. We define the fractional Green's function for the space-time fractionalSchrodinger equation and express it in terms of Fox's H-function and in acomputable series form. The asymptotic formula of the Green's function forlarge argument is also obtained, and applied to study the fractional quantumscattering problem. We get the approximate scattering wave function withcorrection of every order.

Fractional Green's function for the time-dependent scattering problem in the Space-time-fractional quantum mechanics