Abstract

This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam Rassias, and generalized Hyers–Ulam–Rassias stability. We provide some test problems for illustrating our analysis.

中文翻译：

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反周期边界条件下隐式分数阶微分方程的研究

摘要

这项研究工作与研究一类特殊的时滞隐式分数阶微分方程处于反周期边界条件下有关。借助Schauder和Banach提出的经典不动点理论，我们得出了有关至少一个解的存在性的一些结果。此外，我们还研究了一些结果，包括Hyers-Ulam，广义Hyers-Ulam，Hyers-Ulam Rassias和广义Hyers-Ulam-Rassias稳定性。我们提供一些测试问题以说明我们的分析。