We study the initial-boundary value problem for the nonlinear fractional Schrödinger equation {ut+i(uxx+12π∫0∞sign(x−y)|x−y|12uy( y)dy)+i|u|2u=0, t>0, x>0;u(x,0)=u0(x), x>0,ux(0,t)=h(t), t>0.