一类基于Mittag-Leffler函数的非线性高阶Hadamard分数阶Langevin方程积分边问题的存在性和不稳定性

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2304053z

Kaihong Zhao

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引用次数: 10

摘要

朗之万方程是描述粒子随机运动的一个非常重要的数学模型。分数阶朗之万方程是研究复杂粘弹性的有力工具。因此，本文研究了一类具有积分边值条件的非线性高阶Hadamard分数阶Langevin方程。首先，利用逐次逼近和Mittag-Leffler函数将微分方程转化为等效积分方程。然后利用不动点理论得到了解的存在唯一性。同时，通过不等式技术和直接分析证明了Ulam-Hyers (UH)的稳定性。

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Existence and uh-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions

The Langevin equation is a very important mathematical model in describing the random motion of particles. The fractional Langevin equation is a powerful tool in complex viscoelasticity. Therefore, this paper focuses on a class of nonlinear higher-order Hadamard fractional Langevin equation with integral boundary value conditions. Firstly, we employ successive approximation and Mittag-Leffler function to transform the differential equation into an equivalent integral equation. Then the existence and uniqueness of the solution are obtained by using the fixed point theory. Meanwhile, the Ulam-Hyers (UH) stability is proved by inequality technique and direct analysis.

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