Fractional Schrödinger equations with potential and optimal controls. (English) Zbl 1253.35205

Summary: 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.


35R11 Fractional partial differential equations
49J20 Existence theories for optimal control problems involving partial differential equations
35Q93 PDEs in connection with control and optimization
35Q40 PDEs in connection with quantum mechanics
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