In this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory.

中文翻译：

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具有非瞬时脉冲且阶数为α∈（1，2）的非局部分数半线性微分包含

在本文中，我们建立温和解存在非局部分数半线性微分包含顺序的noninstantaneous脉冲α由余弦家族的有界的线性算子∈（1,2）和生成。此外，我们展示了解决方案集的紧凑性。当多值函数的值是凸的和非凸的时，我们都考虑这两种情况。举例说明了该理论。