Fractional Schrödinger equations with potential and optimal controls

In this paper, we study fractional Schrödinger equations with potential and optimal controls. The first novelty is a suitable concept on a mild solution for our problems. Existence, uniqueness, local stability and attractivity, and data continuous dependence of mild solutions are also presented respectively. The second novelty is an initial study on the optimal control problems for the controlled fractional Schrödinger equations with potential. Existence and uniqueness of optimal pairs for the standard Lagrange problem are obtained.