In this paper, by employing some fixed point theory and nonlinear functional analysis, we set up existence and uniqueness of a special class of Hilfer-Katugampola fractional implicit differential equations with nonlocal conditions. Further, we investigate various types of fractional Ulam-Hyers stabilities and uniqueness of ε-approximate for solutions on our concerned problem via the Picard operator method and a generalized Gronwall inequality. In addition, three examples are presented to show the application of our main results.

中文翻译：

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具有非局部条件的Hilfer-Katugampola分数阶隐式微分方程的研究

本文利用一些不动点理论和非线性泛函分析，建立了具有非局部条件的一类特殊的Hilfer-Katugampola分数阶隐式微分方程的存在性和唯一性。此外，我们通过Picard算子方法和广义Gronwall不等式，研究了各种类型的分数阶Ulam-Hyers稳定性和ε-逼近的唯一性，以解决我们关心的问题。此外，还提供了三个示例来说明我们主要结果的应用。