Existence and Hyers–Ulam stability results for nonlinear fractional systems with coupled nonlocal initial conditions

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• 作者：Xiaoyan Li ; Wei Jiang ; Jiangru Xiang
• 关键词：Nonlinear fractional differential equations ; Nonlocal initial conditions ; Hyers–Ulam stability ; Vector ; valued norm ; 26A33 ; 45N05
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：50
• 期：1-2
• 页码：493-509
• 全文大小：446 KB
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• 作者单位：Xiaoyan Li (1)
  Wei Jiang (1)
  Jiangru Xiang (1)
  
  1. School of Mathematical Science, Anhui University, Hefei, 230601, Anhui, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we prove the existence of solutions for two kinds of nonlinear fractional differential systems with coupled nonlocal initial conditions, the approach is based on the fixed point theorem of Perov and the choice of suitable norm for vectors. Further, Hyers–Ulam stability problems are discussed for these two kinds of nonlinear fractional systems. Two examples are presented to illustrate the theory. Keywords Nonlinear fractional differential equations Nonlocal initial conditions Hyers–Ulam stability Vector-valued norm