In this manuscript, we give a partial answer to Reich’s problem on multivalued contraction mappings and generalize Mizoguchi–Takahashi’s fixed point theorem using a new approach of multivalued orthogonal \((\tau ,F)\)-contraction mappings in the framework of orthogonal metric spaces. We give a nontrivial example to prove the validity of our results. Some interesting consequences are also deduced. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

中文翻译：

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正交压缩映射的多值问题及其在分数阶微分方程中的应用

在本手稿中，我们对Reich在多值压缩映射上的问题给出了部分答案，并在正交度量的框架内使用一种新的多值正交\（（\ tau，F）\）-压缩映射的方法来推广Mizoguchi–Takahashi的不动点定理。空格。我们举一个简单的例子来证明我们的结果的有效性。还可以得出一些有趣的结果。最后，作为应用，我们证明了非线性分数阶微分方程解的存在性和唯一性。