Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2025 09 11 A note on Approximate controllability of differential inclusion with non-instantaneous impulses 10014 10.22075/ijnaa.2024.34305.5122 EN Vineet Kumar Chaurasiya Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University Mathura, 281406, India Brijendra Kumar Chaurasiya Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, India Avadhesh Kumar Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, India Journal Article 2024 06 01 The article explores the study of approximation controllability in a particular subset of differential inclusion systems that include non-instantaneous impulses in the Banach space X. By using non-linear alternatives for Kakutani mappings, semi-group theory, and fixed-point theorems. Our approach yields noteworthy conclusions. Furthermore, we provide a concrete example to clarify how the suggested theoretical framework might be used in practice. An investigation of the concept of approximation controllability is crucial for comprehending the dynamics of a system, especially in situations when attaining exact control is difficult. When we consider systems with impulses that do not happen instantly, we face complexity that requires advanced mathematical techniques for a comprehensive examination. Our study expands the theoretical comprehension of controllability in complex systems and provides valuable insights for both theoretical investigation and practical applications in control theory. https://ijnaa.semnan.ac.ir/article_10014_bc1afccdb0cd68a3ca3013da622528f8.pdf