In this paper, we study a nonlinear fractional boundary value problem on a particular metric graph, namely, a circular ring with an attached edge. First, we prove existence and uniqueness of solutions using the Banach contraction principle and Krasnoselskii's fixed point theorem. Further, we investigate different kinds of Ulam-type stability for the proposed problem. Finally, an example is given in order to demonstrate the application of the obtained theoretical results.

中文翻译：

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具有附加边的圆环上的非线性分数边值问题的存在性和稳定性分析：度量图上分数演算的研究。

在本文中，我们研究了特定度量图上的非线性分数边值问题，即带有附加边的圆环。首先，我们使用Banach压缩原理和Krasnoselskii不动点定理证明了解的存在性和唯一性。此外，我们针对提出的问题研究了不同类型的Ulam型稳定性。最后，给出一个例子以证明所获得的理论结果的应用。