Existence of solutions for fractional Langevin equation with infinite-point boundary conditions

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• 作者：Bingxian Li ; Shurong Sun ; Ying Sun
• 关键词：Fractional Langevin equation ; Infinite ; point boundary value problem ; Positive solutions
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：683-692
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we investigate a class of nonlinear Langevin equation involving two fractional orders \(\alpha \in (0,1]\) and \(\gamma \in (1,2]\) with infinite-point boundary value conditions. By Leray–Schauder’s nonlinear alternative and Leray–Schauder degree theory, several new existence results of solutions are obtained. An example is given to show the applicability of our main results.