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

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 solut...

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Published in:AIMS mathematics Vol. 6; no. 4; pp. 3741 - 3760
Main Authors: Wu, Yu-ting, Lan, Heng-you, Liu, Chang-jiang
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2021
Subjects:
existence and uniqueness
fuzzy fractional delay differential equation
fuzzy terms separation method
implicit coupled system
solution algorithm
triangular fuzzy function
ISSN:2473-6988, 2473-6988
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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.
AbstractList 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.
Author Liu, Chang-jiang
Wu, Yu-ting
Lan, Heng-you
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College of Mathematics and Statistics, Sichuan University of Science & Engineering, 643000, Zigong, Sichuan, P. R. China
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StartPage 3741
SubjectTerms existence and uniqueness
fuzzy fractional delay differential equation
fuzzy terms separation method
implicit coupled system
solution algorithm
triangular fuzzy function
Title On implicit coupled systems of fuzzy fractional delay differential equations with triangular fuzzy functions
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Volume 6
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