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Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations

Author

Listed:
  • Humaira

    (Department of Mathematics, University of Malakand, Chakdara Dir(L) 18800, Pakistan)

  • Muhammad Sarwar

    (Department of Mathematics, University of Malakand, Chakdara Dir(L) 18800, Pakistan)

  • Thabet Abdeljawad

    (Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

  • Nabil Mlaiki

    (Department Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

Abstract

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.

Suggested Citation

  • Humaira & Muhammad Sarwar & Thabet Abdeljawad & Nabil Mlaiki, 2021. "Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1969-:d:616336
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    Citations

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    Cited by:

    1. Michal Fečkan & Marius-F. Danca, 2022. "Stability, Periodicity, and Related Problems in Fractional-Order Systems," Mathematics, MDPI, vol. 10(12), pages 1-2, June.
    2. Fan Zhang & Heng-You Lan & Hai-Yang Xu, 2022. "Generalized Hukuhara Weak Solutions for a Class of Coupled Systems of Fuzzy Fractional Order Partial Differential Equations without Lipschitz Conditions," Mathematics, MDPI, vol. 10(21), pages 1-21, October.

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