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α∈(1,2]阶的有限时滞半线性发展方程的近似可控性
马赛赛,寇春海,葛富东
作者单位E-mail
马赛赛 东华大学 理学院, 上海 201620  
寇春海 东华大学 理学院, 上海 201620 kouchunhai@dhu.edu.cn 
葛富东 东华大学 信息学院, 上海 201620  
摘要:
讨论了α∈(1,2]阶的有限时滞半线性发展方程的近似可控性.首先运用压缩映像原理证明了弱解的存在唯一性,进而在适当条件下运用α-阶强连续余弦族理论证明了系统的近似可控性.
关键词:  近似可控性  分数阶发展方程  有限时滞  α-阶余弦族  压缩映像原理
DOI:10.3969/J.ISSN.100-5137.2017.03.006
分类号:
基金项目:This research was supported by Chinese Universities Science Fund (CUSF-DH-D-2014061)
Approximate controllability of semilinear fractional evolution equations of order α∈(1, 2] with finite delay
Ma Saisai,Kou Chunhai,Ge Fudong
Abstract:
This paper considers the approximate controllability of semilinear fractional evolution equations of order α∈ (1, 2] with finite delay. Using the contraction mapping principle, we explore the existence and uniqueness of the mild solution. Furthermore, under certain hypotheses, the approximate controllability is obtained by the theory of strongly continuous-order cosine family. As an illustration of the application of the obtained result, an example is given at last.
Key words:  approximate controllability  fractional evolution equation  finite delay  α-order cosine family  contraction mapping principle