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 - <p style="text-align: justify;">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.</p>