{"ID":2894279,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11058","arxiv_id":"2507.11058","title":"On the optimality conditions for a fractional diffusive equation with a nonlocal term","abstract":"We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 \u003c s \u003c 1$, 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.","short_abstract":"We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 \u003c s \u003c 1$, 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 l...","url_abs":"https://arxiv.org/abs/2507.11058","url_pdf":"https://arxiv.org/pdf/2507.11058v1","authors":"[\"Jasarat Gasimov\",\"Nazim Mahmudov\"]","published":"2025-07-15T07:47:23Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}