具有无穷点边界条件的分数阶朗格万方程:在分数阶谐振子上的应用

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20230124

Lamya Almaghamsi, Ahmed Salem

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引用次数: 0

摘要

本文研究了两个分数阶朗之万方程解的存在唯一性问题。利用无穷点边界条件，研究了边值问题。实现了Banach收缩原理、leray -非线性Schauder替代定理和Leray-Schauder度定理。通过数值算例验证了所得结果的准确性。此外，作为我们研究结果的一个应用，我们计算了一个分数阶谐振子在随机力高斯有色噪声作用下的平均值和方差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR

The current study is concerned with the existence and uniqueness of the solution to the Langevin equation of two separate fractional orders. With the infinite-point boundary condition, the boundary value problem is studied. The Banach contraction principle, Leray-nonlinear Schauder's alternative, and Leray-Schauder degree theorems are all implemented. A numerical example is presented to demonstrate the accuracy of our results. In addition, as an application of our results, the mean and variance of a fractional harmonic oscillator with the undamped angular frequency of the oscillator under the effect of a random force described as Gaussian colored noise are calculated.

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.