In this paper, we investigate the existence of a unique coupled fixed point for admissible mapping which is of contraction in the context of metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.

中文翻译：

---

度量空间中容许收缩的分数混合微分方程和耦合的不动点结果

在本文中，我们研究了可允许映射的唯一耦合不动点的存在度量空间中的收缩。我们还表明，本文介绍的结果将扩展文献中出现的许多最新结果。此外，我们将我们的结果应用于为具有第二类线性摄动和三点边界条件的分数混合微分方程耦合系统解的存在和唯一性开发充分的条件。