RETRACTED: Existence of global solutions for the semilinear nonlocal fractional Cauchy problem of the Schrodinger equation (Retracted Article)

This paper is concerned with the global existence of solutions for the semilinear nonlocal fractional Cauchy problem of the Schrodinger equation. Firstly, based on the Schrodinger approximation technique and the theory of a family of potential wells, the authors obtain the invariant sets and vacuum isolating of global solutions including the critical case. Then, the global existence of solutions and the stability of equilibrium points are discussed. Finally, the global asymptotic stability of the unique positive equilibrium point of the system is proved by applying the Leray-Schauder alternative fixed point theorem.