On the optimality conditions for a fractional diffusive equation with a nonlocal term
Optimization and Control
2025-07-16 v1
Abstract
We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order , incorporating a nonlocal time component modeled by an integral kernel. After establishing well-posedness of the problem, we analyze the properties of the control-to-state operator. We prove the existence of at least one optimal control and derive both first-order and second-order optimality conditions, which ensure local uniqueness. Under further assumptions, we also demonstrate that global uniqueness of the optimal control can be achieved.
Cite
@article{arxiv.2507.11058,
title = {On the optimality conditions for a fractional diffusive equation with a nonlocal term},
author = {Jasarat Gasimov and Nazim Mahmudov},
journal= {arXiv preprint arXiv:2507.11058},
year = {2025}
}