Optimal control of a fractional Sturm–Liouville problem on a star graph. (4th March 2021) - Mophou, Gisèle; Leugering, Günter; Fotsing, Pasquini Soh
ABSTRACT: This paper is devoted to elliptic fractional boundary value problems of Sturm–Liouville type on an interval and on a general star graph. We first give some existence and uniqueness results on an open bounded real interval, prove the existence of solutions to a quadratic boundary optimal control problem and provide a characterization via optimality conditions. We then investigate the analogous problems for a fractional Sturm–Liouville problem on a star graph with mixed Dirichlet and Neumann boundary controls.