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 and Nabil Mlaiki
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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

Mathematics, 2021, vol. 9, issue 16, 1-17

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.

Keywords: complex-valued fuzzy metric space; fuzzy mappings; fixed-point; cauchy sequence and contractive condition; least upper bound property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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