Local well-posedness of semilinear space-time fractional Schrödinger equation

The semilinear space-time fractional Schrodinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox H-functions in order to establish some L s decay estimates. After that, we give some space-time estimates for the mild solutions from which the local well-posedness is derived on some proper Banach space.