{"title":"FRACTIONAL LANGEVIN EQUATIONS WITH INFINITE-POINT BOUNDARY CONDITION: APPLICATION TO FRACTIONAL HARMONIC OSCILLATOR","authors":"Lamya Almaghamsi, Ahmed Salem","doi":"10.11948/20230124","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":48811,"journal":{"name":"Journal of Applied Analysis and Computation","volume":"60 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Analysis and Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11948/20230124","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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