In this paper, we prove two results concerning the existence of S-asymptotically ω-periodic solutions for non-instantaneous impulsive semilinear differential inclusions of order \(1<\alpha <2\) and generated by sectorial operators. In the first result, we apply a fixed point theorem for contraction multivalued functions. In the second result, we use a compactness criterion in the space of bounded piecewise continuous functions defined on the unbounded interval \(J=[0,\infty )\). We adopt the fractional derivative in the sense of the Caputo derivative. We provide three examples illustrating how the results can be applied.

中文翻译：

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具有扇形算子的分数非瞬时脉冲半线性微分包含解的渐近周期行为

在本文中，我们证明了关于S渐近ω周期解的存在性的两个结果，用于阶\(1<\alpha <2\)并由扇形算子生成的非瞬时脉冲半线性微分包含。在第一个结果中，我们将不动点定理应用于收缩多值函数。在第二个结果中，我们在无界区间\(J=[0,\infty )\)上定义的有界分段连续函数的空间中使用紧凑性标准。我们采用 Caputo 导数意义上的分数导数。我们提供了三个示例来说明如何应用结果。