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 inAIMS mathematics Vol. 6; no. 4; pp. 3741 - 3760
Main Authors Wu, Yu-ting, Lan, Heng-you, Liu, Chang-jiang
Format Journal Article
LanguageEnglish
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
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ISSN2473-6988
2473-6988
DOI10.3934/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.
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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CorporateAuthor 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
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
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Title On implicit coupled systems of fuzzy fractional delay differential equations with triangular fuzzy functions
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