Fractional nonlinear Schrödinger and Hartree equations in modulation spaces

We establish global well-posedness for the mass subcritical nonlinear fractional Schrödinger equation $$i{u}_t-(-\mathrm{\Delta }{)}^{\frac{\beta }{2}}u+F(u)=0$$ having radial initial data in modulation spaces $M^{p,\frac{p}{p-1}}({\mathbb{R}}^n)$ for $n\ge 2,p>2$ and $p$ sufficiently close to $2.$ The nonlinearity $F(u)$ is either of power-type $F(u)=\pm (\mathrm{\mid }u{\mathrm{\mid }}^{\alpha }u)(0<\alpha <2\beta \mathrm{/}n)$ or Hartree-type $(\mathrm{\mid }x{\mathrm{\mid }}^{-\nu }\ast \mathrm{\mid }u{\mathrm{\mid }}^2)u(0<\nu <\min \{\beta ,n\})\mathrm{.}$ Our order of dispersion $\beta$ lies in $(2n\mathrm{/}(2n-1),2)\mathrm{.}$