Novel fixed point technique to coupled system of nonlinear implicit fractional differential equations in complex valued fuzzy rectangular $ b $-metric spaces

Sumaiya Tasneem Zubair; Kalpana Gopalan; Thabet Abdeljawad; Nabil Mlaiki; Sumaiya Tasneem Zubair; Kalpana Gopalan; Thabet Abdeljawad; Nabil Mlaiki

doi:10.3934/math.2022608

AIMS Mathematics

2022, Volume 7, Issue 6: 10867-10891. doi: 10.3934/math.2022608

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Research article

Novel fixed point technique to coupled system of nonlinear implicit fractional differential equations in complex valued fuzzy rectangular $ b $-metric spaces

1.
Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Chennai-603 110, India
2.
Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 14 February 2022 Revised: 14 March 2022 Accepted: 16 March 2022 Published: 01 April 2022
MSC : 47H10, 54H25, 26A33, 34B27

The fundamental purpose of this research is to investigate the existence theory as well as the uniqueness of solutions to a coupled system of fractional order differential equations with Caputo derivatives. In this regard, we utilize the definition and properties of a newly developed conception of complex valued fuzzy rectangular $ b $-metric spaces to explore the fuzzy form of some significant fixed point and coupled fixed point results. We further present certain examples and a core lemma in the case of complex valued fuzzy rectangular $ b $-metric spaces.
- complex valued fuzzy rectangular $ b $-metric spaces,
- fixed point,
- Green's function,
- implicit coupled system,
- existence theory
Citation: Sumaiya Tasneem Zubair, Kalpana Gopalan, Thabet Abdeljawad, Nabil Mlaiki. Novel fixed point technique to coupled system of nonlinear implicit fractional differential equations in complex valued fuzzy rectangular $ b $-metric spaces[J]. AIMS Mathematics, 2022, 7(6): 10867-10891. doi: 10.3934/math.2022608

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Abstract

The fundamental purpose of this research is to investigate the existence theory as well as the uniqueness of solutions to a coupled system of fractional order differential equations with Caputo derivatives. In this regard, we utilize the definition and properties of a newly developed conception of complex valued fuzzy rectangular $ b $-metric spaces to explore the fuzzy form of some significant fixed point and coupled fixed point results. We further present certain examples and a core lemma in the case of complex valued fuzzy rectangular $ b $-metric spaces.

References

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