This article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch’s and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results.

中文翻译：

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Caputo-Fabrizio分数阶微分方程隐式Dirichlet边值问题的定性分析

本文研究了在Dirichlet边界条件（DBC）下涉及Caputo-Fabrizio分数阶导数的一类隐式分数阶微分方程。利用Banch和Krasnoselskii提出的经典不动点理论技术，对存在解的相关问题进行了定性分析。此外，还针对提出的问题研究了有关Ulam型稳定性的一些结果。给出了一些相关的例子来证明结果的合理性。