文章基本信息

标题：Unique solution for a new system of fractional differential equations
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作者：Chengbo Zhai ; Xiaolin Zhu
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-19
DOI：10.1186/s13662-019-2330-y
出版社：Hindawi Publishing Corporation
摘要：This paper is devoted to the dynamical behavior of stochastic coupled suspension bridge equations of Kirchhoff type. For the deterministic cases, there are many classical results such as existence and uniqueness of a solution and long-term behavior of solutions. To the best of our knowledge, the existence of random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type is not yet considered. We intend to investigate these problems. We first obtain the dissipativeness of a solution in higher-energy spaces H3(U)×H10(U)×(H2(U)∩H10(U))×H10(U). This implies that the random dynamical system generated by the equation has a random attractor in (H2(U)∩H10(U))×L2(U)×H10(U)×L2(U), which is a tempered random set in the space in H3(U)×H10(U)×(H2(U)∩H10(U))×H10(U).
关键词：Existence and uniqueness; Fractional differential system; Ψ-(h, e)-concave operator