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

Abstract

The semilinear space-time fractional Schrödinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to 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.

23pages

References in corpus (2)

• Fractional Quantum Mechanics
• Well-posedness of the Cauchy problem for the fractional power dissipative equations