On the solutions to the space-time fractional nonlinear Schrodinger equation and their dispersion
We consider the space-time fractional nonlinear Schrodinger equation. We first give a decay estimates and Holder-type estimates of the evolution operators and estimates the nonlinearity in some Sobolev spacs and Besov spaces using the harmonic tools. Then we give a priori estimates of the solution. After that we prove the local and global well-posedness of the solution and its dispersion in some significant spaces.