A Uniform Method to Ulam–Hyers Stability for Some Linear Fractional Equations

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• 作者：JinRong Wang ; Xuezhu Li
• 关键词：Ulam–Hyers stability ; Ulam–Hyers–Rassias stability ; fractional differential equations ; fractional evolution equations ; Mittag ; Leffler functions
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：13
• 期：2
• 页码：625-635
• 全文大小：507 KB
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• 作者单位：JinRong Wang (1)
  Xuezhu Li (1)
  
  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper, we first utilize fractional calculus, the properties of classical and generalized Mittag-Leffler functions to prove the Ulam–Hyers stability of linear fractional differential equations using Laplace transform method. Meanwhile, Ulam–Hyers–Rassias stability result is obtained as a direct corollary. Finally, we apply the same techniques to discuss the Ulam’s type stability of fractional evolution equations, impulsive fractional evolutions equations and Sobolev-type fractional evolution equations.