{"ID":2891807,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16560","arxiv_id":"2507.16560","title":"Study on Control Problem of a Impulsive Neutral Integro-Differential Equations with Fading Memory","abstract":"This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the establishment of mild solutions in the semilinear setting. The approach involves constructing a resolvent family for the corresponding integro-differential equation of linear type without memory. The results for the linear system are established first, then extended to the semilinear scenario, followed by a detailed example to illustrate the theoretical findings.","short_abstract":"This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the establishment of mild solutions in the semilinear setting. The approach involves construc...","url_abs":"https://arxiv.org/abs/2507.16560","url_pdf":"https://arxiv.org/pdf/2507.16560v1","authors":"[\"Garima Gupta\",\"Jaydev Dabas\"]","published":"2025-07-22T13:13:12Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\"]","methods":"[]","has_code":false}