Existence of solutions for implicit fuzzy differential inclusions

doi:10.1007/s10483-015-1914-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (3): 401-416.doi: https://doi.org/10.1007/s10483-015-1914-6

• • 上一篇

Existence of solutions for implicit fuzzy differential inclusions

Chao MIN^1,2, Nanjing HUANG³, Zhibin LIU^1,2, Liehui ZHANG¹

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

收稿日期:2014-04-02 修回日期:2014-08-15 出版日期:2015-03-01 发布日期:2015-03-01
通讯作者: Nanjing HUANG E-mail:nanjinghuang@hotmail.com
基金资助:
Project supported by the National Science Fund for Distinguished Young Scholars of China (No. 51125019), the National Natural Science Foundation of China (No. 11171237), and the Scientific Research Fund of Sichuan Provincial Education Department (No. 11ZA024)

Existence of solutions for implicit fuzzy differential inclusions

Chao MIN^1,2, Nanjing HUANG³, Zhibin LIU^1,2, Liehui ZHANG¹

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

Received:2014-04-02 Revised:2014-08-15 Online:2015-03-01 Published:2015-03-01
Contact: Nanjing HUANG E-mail:nanjinghuang@hotmail.com
Supported by:
Project supported by the National Science Fund for Distinguished Young Scholars of China (No. 51125019), the National Natural Science Foundation of China (No. 11171237), and the Scientific Research Fund of Sichuan Provincial Education Department (No. 11ZA024)

摘要/Abstract

摘要： 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.

关键词: fuzzy differential equation (FDE), implicit fuzzy differential inclusion (IFDI), stacking theorem, selection theorem

Abstract: 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.

Key words: fuzzy differential equation (FDE), implicit fuzzy differential inclusion (IFDI), stacking theorem, selection theorem

中图分类号:

Chao MIN;Nanjing HUANG;Zhibin LIU;Liehui ZHANG. Existence of solutions for implicit fuzzy differential inclusions[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 401-416.

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Existence of solutions for implicit fuzzy differential inclusions

Existence of solutions for implicit fuzzy differential inclusions

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