In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag–Leffler functions. The existence and uniqueness results are established by using Schauder's fixed point theorem and Banach's fixed point theorem, respectively. An example is given to illustrate the main results.

中文翻译：

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通过 Mittag-Leffler 函数求解具有两个 Hadamard 分数导数的 Langevin 方程

在本文中，我们讨论了具有两个 Hadamard 分数导数的 Langevin 方程的可解性。本次讨论的方法是研究等效沃尔泰拉积分方程的米塔格-莱弗勒函数的解。分别利用Schauder不动点定理和Banach不动点定理建立了存在性和唯一性结果。举一个例子来说明主要结果。