This article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative known as the fractional derivative with respect to another function.

中文翻译：

---

应用到广义分数阶微分方程的对称收缩研究

本文在完全 F 度量空间的框架内提出了四种不同的对称收缩。我们检查条件以保证这些收缩的不动点的存在性和唯一性。作为一个应用，我们寻找分数边值问题的解，该问题涉及广义分数阶导数，称为相对于另一个函数的分数阶导数。