Our aim in this paper is to give a sufficient condition ensuring the finite-time attractivity for the zero solution to semilinear functional differential inclusions in Banach spaces, in the case where the nonlinearity function possibly has superlinear growth. Our analysis is based on the semigroup theory, the fixed point principle for condensing multi-valued maps, and local estimates of solutions. The abstract results will be applied to a class of polytope inclusions in \(C_0\) setting.

中文翻译：

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一类具有有限时滞的分数阶微分包含解的有限时间吸引性

我们的目标是在非线性函数可能具有超线性增长的情况下，提供一个充分的条件，以确保Banach空间中半线性泛函微分包含零解的有限时间吸引性。我们的分析基于半群理论，压缩多值映射的不动点原理以及解的局部估计。抽象结果将应用于\（C_0 \）设置中的一类多表位包含物。