This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms). An example and some corollaries are derived to strengthen our main theoretical results. We end the manuscript with two important applications, one of them is interested in finding a solution to the system of nonlinear integral equations (nie) and the other one relies on the existence of a solution to fractional integral equations (fie).

中文翻译：

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具有应用程序的广义图形保留多值映射的新重合点结果

本研究旨在调查广义多值收缩 (gmc) 映射的新重合点 (cp)，该映射涉及b度量空间 (b-ms) 中的有向图。推导出一个例子和一些推论来加强我们的主要理论结果。我们以两个重要的应用结束手稿，其中一个对找到非线性积分方程组 (nie) 的解感兴趣，另一个依赖于分数积分方程 (fie) 的解的存在。