Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

Abstract

In this paper, we investigate the distributed optimal control problem for time-fractional differential system involving Schrödinger operator defined on Rn. 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.