Volume 6, Issue 2
Fractional Langevin Equation at Resonance

Zhiyuan Liu & Shurong Sun

J. Nonl. Mod. Anal., 6 (2024), pp. 288-304.

Published online: 2024-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The study of fractional Langevin equation has obtained abundant results in recent years. However, there are few studies on resonant fractional Langevin equation. In this paper, we investigate boundary value problems for fractional Langevin equation at resonance. By virtue of Banach contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the uniqueness and existence of solutions. In addition, we get different stability results, including Ulam-Hyres stability and generalized Ulam-Hyres stability. Finally, give relevant examples to demonstrate the main results.

  • AMS Subject Headings

26A33, 82C31, 34F15, 39A27, 47H10

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COPYRIGHT: © Global Science Press

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@Article{JNMA-6-288, author = {Liu , Zhiyuan and Sun , Shurong}, title = {Fractional Langevin Equation at Resonance}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {2}, pages = {288--304}, abstract = {

The study of fractional Langevin equation has obtained abundant results in recent years. However, there are few studies on resonant fractional Langevin equation. In this paper, we investigate boundary value problems for fractional Langevin equation at resonance. By virtue of Banach contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the uniqueness and existence of solutions. In addition, we get different stability results, including Ulam-Hyres stability and generalized Ulam-Hyres stability. Finally, give relevant examples to demonstrate the main results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.288}, url = {http://global-sci.org/intro/article_detail/jnma/23176.html} }
TY - JOUR T1 - Fractional Langevin Equation at Resonance AU - Liu , Zhiyuan AU - Sun , Shurong JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 288 EP - 304 PY - 2024 DA - 2024/06 SN - 6 DO - http://doi.org/10.12150/jnma.2024.288 UR - https://global-sci.org/intro/article_detail/jnma/23176.html KW - Fractional order, Langevin equation, resonance, boundary value problems, fixed point theorem. AB -

The study of fractional Langevin equation has obtained abundant results in recent years. However, there are few studies on resonant fractional Langevin equation. In this paper, we investigate boundary value problems for fractional Langevin equation at resonance. By virtue of Banach contraction mapping principle and Leray-Schauder fixed point theorem, we obtain the uniqueness and existence of solutions. In addition, we get different stability results, including Ulam-Hyres stability and generalized Ulam-Hyres stability. Finally, give relevant examples to demonstrate the main results.

Liu , Zhiyuan and Sun , Shurong. (2024). Fractional Langevin Equation at Resonance. Journal of Nonlinear Modeling and Analysis. 6 (2). 288-304. doi:10.12150/jnma.2024.288
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