Optimal control problems of parabolic fractional sturm liouville equations in a star graph

Abstract

In the present paper we deal with parabolic fractional initial-boundary value problems of Sturm-Liouville type in an interval and in a general star graph. We first give several existence, uniqueness and regularity results of weak and very-weak solutions. We prove the existence and uniqueness of solutions to a quadratic boundary optimal control problem and provide a characterization of the optimal contol via the Euler-Lagrange first order optimality conditions. We then investigate the analogous problems for a fractional Sturm-Liouville problem in a general star graph with mixed Dirichlet and Neumann boundary controls. The existence and uniqueness of minimizers, and the characterization of the first order optimality conditions are obtained in a general star graph by using the method of Lagrange multipliers.

Distributed optimal control problems driven by space-time fractional parabolic equations

“…Before we embark on the proof of Theorem 3.1, we first recall a result from Leugering et al (2021) regarding the continuity and coercivity of the bilinear form a(t, •, •). Then, we discuss a method to approximate the kernel g 1−α of the Caputo fractional derivative, followed by the basic identity (Lemma 3.2) for kernels.…”

“…Recently, Leugering et al (2021) studied the optimal control problems associated with space fractional parabolic problems of Sturm-Liouville type in an interval and on a star graph. The authors proved the existence and uniqueness of solutions for the governing equations and the fractional optimal control problems.…”