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Distributed control for time-fractional differential system involving Schrödinger operator. (English) Zbl 1422.49006

Summary: In this paper, we investigate the distributed optimal control problem for time-fractional differential system involving Schrödinger operator defined on \(\mathbb{R}^n\). The time-fractional derivative is considered in the Riemann-Liouville sense. By using the Lax-Milgram lemma, we prove the existence and uniqueness of the solution of this system. For the fractional Dirichlet problem with linear quadratic cost functional, we give some equations and inequalities which provide the necessary and sufficient optimality conditions. Moreover, we provide specific application examples to demonstrate the effectiveness of our results.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
49N10 Linear-quadratic optimal control problems
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