Periodic problem of first order nonlinear uncertain dynamic systems

Volume 10, Issue 12, pp 6288--6297 http://dx.doi.org/10.22436/jnsa.010.12.13

Publication Date: December 09, 2017 Submission Date: October 19, 2017

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Authors

Yongzhao Wang - School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China. Qian Liu - School of Civil Engineering and Architecture, Anyang University, Anyang, 455000, China. Qiansheng Feng - Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, 223003, China.

Abstract

The solution to fuzzy differential equation is very important for solving the uncertainly practical problems in the real world. In this paper, the definition of solution for periodic problems of fuzzy differential equations based on the theory of differential inclusions is given. Using the theory of differential inclusions, function analysis and Kakutani Fixed point theorem, an existence theorem of periodic solutions to first order uncertain dynamical systems is obtained in a more general set.

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Keywords

• Fuzzy number
• uncertain dynamical system
• Kakutani fixed point theorem
• differential inclusion

MSC

•  47H05
•  47H09
•  47H10

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