Lagrange problem for fractional ordinary elliptic system via Dubovitskii–Milyutin method

Abstract

In the paper, we investigate a weak maximum principle for Lagrange problem described by a fractional ordinary elliptic system with Dirichlet boundary conditions. The Dubovitskii–Milyutin approach is used to find the necessary conditions. The fractional Laplacian is understood in the sense of Stone–von Neumann operator calculus.

Keywords

• fractional Laplacian
• Dirichlet boundary conditions
• optimal control
• maximum principle, Dubovitskii–Milyutin theorem