On implicit coupled systems of fuzzy fractional delay differential equations with triangular fuzzy functions

Yu-ting Wu; Heng-you Lan; Chang-jiang Liu; Yu-ting Wu; Heng-you Lan; Chang-jiang Liu

doi:10.3934/math.2021222

AIMS Mathematics

2021, Volume 6, Issue 4: 3741-3760. doi: 10.3934/math.2021222

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On implicit coupled systems of fuzzy fractional delay differential equations with triangular fuzzy functions

1.
College of Mathematics and Statistics, Sichuan University of Science & Engineering, 643000, Zigong, Sichuan, P. R. China
2.
South Sichuan Center for Applied Mathematics, and Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, 643000, Zigong, Sichuan, P. R. China

Received: 07 October 2020 Accepted: 17 January 2021 Published: 26 January 2021
MSC : 34A08, 39A26, 34K32, 34A12

In this paper, we introduce and study an implicit coupled system of fuzzy fractional 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 the solution of the implicit coupled system 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 implicit coupled systems. Further, we prove existence and uniqueness of solution for the considered systems, and also construct a solution algorithm. Finally, an example is given to illustrate our main results and some further work are presented.
- existence and uniqueness,
- implicit coupled system,
- fuzzy fractional delay differential equation,
- triangular fuzzy function,
- fuzzy terms separation method,
- solution algorithm
Citation: Yu-ting Wu, Heng-you Lan, Chang-jiang Liu. On implicit coupled systems of fuzzy fractional delay differential equations with triangular fuzzy functions[J]. AIMS Mathematics, 2021, 6(4): 3741-3760. doi: 10.3934/math.2021222

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Abstract

In this paper, we introduce and study an implicit coupled system of fuzzy fractional 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 the solution of the implicit coupled system 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 implicit coupled systems. Further, we prove existence and uniqueness of solution for the considered systems, and also construct a solution algorithm. Finally, an example is given to illustrate our main results and some further work are presented.

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