Changyou Wang1, Xiaojuan Zhao1, Lili Jia2,*, Tao Jiang3
1College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China.
2Dianchi College of Yunnan University, Kunming, Yunnan 650228, China.
3School of Control Engineering, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China.
*Corresponding author: Lili Jia
Abstract
At present, the difference equations studied by most scholars are ordinary difference equations with real parameters and initial values. However, for the difference equation describing many natural phenomena, the parameter information is uncertain, incomplete and fuzzy. Based on the above fact, if the parameters and initial values in the ordinary difference equation model are transformed into fuzzy numbers, the research on the existence and uniqueness of its solution will have greater practical value and significance. In this paper, a class of seven-order exponential fuzzy difference equations is studied. Firstly, the fuzzy difference equation is transformed into the corresponding ordinary difference equations with parameter by using the fuzzy set theory, in which the value range of the parameter is 0 to 1. Then, by using iterative method, inequality technique and mathematical induction, the existence and uniqueness of solutions of ordinary differential equations are obtained. Thus, the existence and uniqueness for the solution of the exponential fuzzy difference equation is proved.
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