This manuscript is mainly focusing on the approximate controllability of fractional differential evolution inclusions of order 1 < r < 2 with infinite delay. We study our primary outcomes by using the theoretical concepts about fractional calculus, cosine, and sine function of operators and Dhage’s fixed point theorem. Initially, we prove the approximate controllability for the fractional evolution system. The results are established under the assumption that the associated linear system is approximately controllable. Then, we develop our conclusions to the ideas of nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study.

该手稿主要关注 具有无限延迟的1 < r <2阶分数阶微分演化包含物的近似可控性 。我们通过使用关于分数微积分，余弦和运算符的正弦函数以及Dhage不动点定理的理论概念来研究主要结果。最初，我们证明了分数演化系统的近似可控性。在相关线性系统近似可控的假设下建立结果。然后，我们对非本地条件的想法得出结论。最后，我们提出理论和实际应用以支持研究的有效性。