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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Veröffentlicht in:Fuzzy sets and systems Jg. 470; S. 108669
Hauptverfasser: Wang, Chao, Zheng, Xin, Li, Zhien, Agarwal, Ravi P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 30.10.2023
Schlagworte:
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
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Zusammenfassung: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