Optimal control problems governed by time-fractional diffusion equations with control constraint

TL;DR

This paper investigates optimal control problems governed by linear time-fractional diffusion equations with control constraints, establishing existence results and deriving first- and second-order optimality conditions.

Contribution

It introduces new existence results and optimality conditions specifically for control problems involving time-fractional diffusion equations.

Findings

Existence of strong solutions to the state equation.

Existence of optimal control solutions.

Derivation of first- and second-order optimality conditions.

Abstract

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of optimal solutions for the optimal control problem. Then we derive first-and second-order optimality conditions for locally optimal solutions to the problem.