This paper describes the required and adequate conditions for controllability and optimal controls of Atangana–Baleanu–Caputo (ABC) neutral fractional integrodifferential equations (NFIE) with noninstantaneous impulses. Measure of noncompactness, semigroup theory, fractional calculus and fixed point techniques act as the main tools in deriving the results. An illustration is offered to enhance our theoretical outcomes.

中文翻译：

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关于非瞬时脉冲 ATANGANA-BALEANU-CAPUTO 中性分数阶积分微分系统可控性的说明

本文描述了具有非瞬时脉冲的 Atangana-Baleanu-Caputo (ABC) 中性分数阶积分微分方程 (NFIE) 的可控性和最优控制的必要和充分条件。非紧性测度、半群论、分数阶微积分和不动点技术是得出结果的主要工具。提供了一个例子来增强我们的理论成果。