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

被引：4

作者：

Almaghamsi, Lamya ^{[1
]}

Salem, Ahmed ^{[2
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

[2] Univ Jeddah, Coll Sci, Dept Math, POB 80327, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2023年 / 13卷 / 06期

关键词：

Fractional Langevin equations; fixed point theorem; existence and uniqueness; infinite-point boundary condition; mean; and variance; EXISTENCE;

D O I：

10.11948/20230124

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3504 / 3523

页数：20

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