Fractional derivatives of fuzzy complex-variable functions and application to fuzzy fractional complex differential equations

In this paper, through theory of fuzzy complex analysis, we introduce some representations of r-cuts of trivial fuzzy zero, nontrivial fuzzy zero and fuzzy complex numbers in polar form on complex plane and establish some of their basic properties. Based on this, the addition and scalar multiplicati...

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Bibliographic Details
Published in:	Fuzzy sets and systems Vol. 470; p. 108669
Main Authors:	Wang, Chao, Zheng, Xin, Li, Zhien, Agarwal, Ravi P.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 30.10.2023
Subjects:	Fractional calculus Fuzzy complex-variable functions Fuzzy fractional complex differential equations Fuzzy fractional Ortigueira derivative Fuzzy fractional complex differential equations Fuzzy complex-variable functions Fuzzy fractional Ortigueira derivative Fractional calculus
ISSN:	0165-0114
Online Access:	Get full text
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Summary:	In this paper, through theory of fuzzy complex analysis, we introduce some representations of r-cuts of trivial fuzzy zero, nontrivial fuzzy zero and fuzzy complex numbers in polar form on complex plane and establish some of their basic properties. Based on this, the addition and scalar multiplication operations of fuzzy complex numbers are established and the calculus of fuzzy complex-variable functions is studied. Moreover, we introduce a notion of fuzzy Ortigueira fractional derivative of fuzzy complex-variable functions and develop a theory of fuzzy fractional calculus on complex plane including some geometric features. As applications, the existence and uniqueness theorem of solutions for nonlinear fuzzy fractional complex-variable differential equations is established and some examples are provided.
ISSN:	0165-0114
DOI:	10.1016/j.fss.2023.108669