Fractional Langevin Equation at Resonance (Journal of Nonlinear Modeling and Analysis, 2024)
The study of fractional Langevin equation has obtained abundantresults in recent years. However, there are few studies on resonant fractionalLangevin equation. In this paper, we investigate boundary value problems forfractional Langevin equation at resonance. By virtue of Banach contractionmapping principle and Leray-Schauder fixed point theorem, we obtain theuniqueness and existence of solutions. In addition, we get different stabilityresults, including Ulam-Hyres stability and generalized Ulam-Hyres stability.Finally, give relevant examples to demonstrate the main results.
Keywords: Fractional order; Langevin equation; resonance; boundary value problems; fixed point theorem.