Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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SOLUTIONS OF A CLASS OF COUPLED SYSTEMS OF FUZZY DELAY DIFFERENTIAL EQUATIONS

  • Wu, Yu-ting (College of Mathematics and Statistics, Sichuan University of Science & Engineering) ;
  • Lan, Heng-you (College of Mathematics and Statistics, Sichuan University of Science & Engineering, South Sichuan Center for Applied Mathematics, and Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing) ;
  • Zhang, Fan (College of Mathematics and Statistics, Sichuan University of Science & Engineering)
  • Received : 2020.10.29
  • Accepted : 2021.02.19
  • Published : 2021.09.15
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Abstract

The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.

Keywords

Acknowledgement

We would like to thank the anonymous referees and editor for their constrictive comments and valuable suggestions. This work was partially supported by the Innovation Fund of Postgraduate, Sichuan University of Science & Engineering (y2020080), the Sichuan Science and Technology Program (2019YJ0541) and the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (2019QZJ03).

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