In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

中文翻译：

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具有非局部积分和反周期型边界条件的分式朗格文方程解的存在性和稳定性分析

在本文中，我们处理具有非局部积分和反周期型边界条件的具有不同阶分数导数的非线性朗之万分数微分方程 (FDE) 解的存在性和唯一性 (EU)。此外，我们研究了解决方案的 Hyres-Ulam (HU) 稳定性。应用Krasnoselskii不动点定理推导出存在结果，应用Banach压缩映射原理确定结果的唯一性。提供了一个例子来确保我们获得的结果的有效性。