Existence of solutions for implicit fuzzy differential inclusions

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• 作者：Chao Min (1) (2)
  Nanjing Huang (3)
  Zhibin Liu (1) (2)
  Liehui Zhang (1)
  
  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation ; Chengdu ; 610059 ; China
  2. School of Science ; Southwest Petroleum University ; Chengdu ; 610500 ; China
  3. Department of Mathematics ; Sichuan University ; Chengdu ; 610064 ; China
  
• 关键词：implicit fuzzy differential inclusion (IFDI) ; fuzzy differential equation (FDE) ; selection theorem ; stacking theorem ; O159 ; O175 ; O177 ; 34A07 ; 47H04 ; 47S40
• 刊名：Applied Mathematics and Mechanics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：36
• 期：3
• 页码：401-416
• 全文大小：377 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics
  Mathematical Modeling and IndustrialMathematics
  Chinese Library of Science
  
• 出版者：Shanghai University, in co-publication with Springer
• ISSN：1573-2754

文摘

A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions (FDIs) and fuzzy differential equations (FDEs), which might be helpful in the analysis of fuzzy dynamic systems.