The purpose of this work is to introduce a new class of implicit relation and implicit type contractive condition in metric spaces under -distance functional. Further, we derive fixed point results under a new class of contractive condition followed by three suitable examples. Next, we discuss results about weak well-posed property, weak limit shadowing property, and generalized -Ulam-Hyers stability of the mappings of a given type. Finally, we obtain sufficient conditions for the existence of solutions for fractional differential equations as an application of the main result.

中文翻译：

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距离下度量空间的一种隐式关系法及其在分数阶微分方程中的应用

这项工作的目的是介绍一类新的隐含关系和隐式类型收缩状态下度量空间-距离的功能。此外，我们在一类新的收缩条件下得出不动点结果，然后是三个合适的例子。接下来，我们讨论关于弱适定性质、弱极限阴影性质和给定类型映射的广义- Ulam-Hyers 稳定性的结果。最后，我们得到了分数阶微分方程解存在的充分条件，作为主要结果的应用。