RESERACH ANNOUNCEMENTS Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrdinger Equation

It is well known that Feynman and Hibbs used path integrals over Brownian paths to derive the standard(nonfractional)Schr(?)dinger equation.Recently,Laskin showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization

It is well known that Feynman and Hibbs used path integrals over Brownian paths to derive the standard（nonfractional） SchrSdinger equation. Recently, Laskin showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known SchrSdinger equation, then the path integral over Lévy trajectories leads to the fractional SchrSdinger equation. Laskin showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu studied some physical applications of the fractional Schr6dinger equation.