Dispersive estimates for time and space fractional Schrödinger equations

Abstract

In this paper, we consider the Cauchy problem for the fractional Schrödinger equation $i{D}_t^{\alpha }u+(-\Delta {)}^{\frac{\beta }{2}}u=0$ with $0<\alpha <1$, $\beta >0$. We establish the dispersive estimates for the solutions. In particular, we prove that the decay rates are sharp.

arXiv comment11 pages

References in corpus (4)

• Fractional Schrodinger equation
• Fractional Quantum Mechanics
• Time Fractional Quantum Mechanics
• Time Fractional Schrödinger Equation; Fox's H-functions and the Effective Potential