Sivaranjani RamasamyThangavelu SenthilprabuKulandhaivel KarthikeyanPalanisamy GeethaSaowaluck ChasreechaiThanin Sitthiwirattham2025-07-072025-07-072025AIMS Mathematics2473698810.3934/MATH.20252002-s2.0-105001676993https://repository.dusit.ac.th/handle/123456789/7317In this article, the necessary and sufficient conditions for the existence and uniqueness of the mild solutions for nonlinear neutral implicit integro-differential equations of non-integer order 0 < α < 1 in the sense of ABC derivative with impulses, delay, and integro initial conditions were established. The existence results were derived using the semi-group theory, measures of non-compactness, and the fixed-point theory in the sense of Arzelà–Ascoli theorem and Schauder’s fixed-point theorem. We analyzed the controllability results of the proposed problem by incorporating the ideas of semi-group theory and fixed-point techniques. The Banach contraction principle was used to derive the uniqueness and controllability of the proposed problem. We provide an example to support the theoretical results. © 2025 the Author(s), licensee AIMS Press.controllabilityfractional derivativeimplicit neutral differential equationssemi-group and fixed point theoriesArticleScopus