  This paper studies the inhomogeneous fractional Sch\"odinger equation $$i\dot
u-(-\Delta)^s u=\pm(I_\alpha *|\cdot|^b|u|^p)|x|^b|u|^{p-2}u.$$ In the mass
super-critical and energy sub-critical regimes, using a Gagliardo-Nirenberg
adapted to the above problem, the standing waves give a sharp threshold of
global existence versus finite time blow-up of solutions.
