Optimal control of a fractional Sturm–Liouville problem on a star graph
Gisèle Mophou, Günter Leugering, Pasquini Soh Fotsing
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.
Topics & Concepts
MathematicsSturm–Liouville theoryUniquenessBounded functionBoundary value problemStar (game theory)GraphInterval (graph theory)Quadratic equationApplied mathematicsMathematical analysisPure mathematicsDiscrete mathematicsCombinatoricsGeometryAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations AnalysisStability and Controllability of Differential Equations