Fractional Langevin Equation at Resonance |
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| Authors: | Zhiyuan Liu Shurong Sun |
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| Affiliation: | School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China |
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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. |
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| Keywords: | Fractional order Langevin equation resonance boundary value problems fixed point theorem |
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