Mathematics (Aug 2021)

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

  • Humaira,
  • Muhammad Sarwar,
  • Thabet Abdeljawad,
  • Nabil Mlaiki

DOI
https://doi.org/10.3390/math9161969
Journal volume & issue
Vol. 9, no. 16
p. 1969

Abstract

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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.

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