The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness (EU) of solutions for the prescribed equations are defined. Our viewpoint is built on the specification of the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is offered to smooth the comprehension of the hypothetical outcomes.

中文翻译：

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分数拉格文方程的解和存在性理论的稳定性分析

本文介绍了分数朗格文方程（FDEs），其中涉及与非局部积分和非周期性边界条件有关的独立阶的Caputo Hadamard导数。规定方程的解的稳定性，存在性和唯一性（EU）。我们的观点建立在Krasnoselskii不动点定理的规范和Banach压缩映射原理的基础上。提供了一个应用程序，以使对假设结果的理解更加流畅。