In this manuscript, hybrid common fixed point results in the setting of a -metric space are established. Our results generalized the results of Fisher, Khan, and Piri et al. for set-valued mapping in -metric spaces. Applications to forced damped oscillations, infinite systems of fractional order differential equations, and system of functional equations are also studied. We construct an example to support our main result.

中文翻译：

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混合不动点定理及其在强迫阻尼振动和分数阶微分方程无穷大系统中的应用

在该手稿，混合共同固定在的设定点的结果-度量空间成立。我们的结果概括了Fisher，Khan和Piri等人的结果。集值映射中-度量空间。还研究了强制阻尼振荡，分数阶微分方程的无限系统和功能方程组的应用。我们构造一个例子来支持我们的主要结果。