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.
Highlights
It is a well-known fact that metric fixed-point theory is developed by Banach fixedpoint theorem
The advances made in fixed-point theory are applied to differential equations and integral equations
We considered a complex fuzzy set in fuzzy metric spaces, which is more general than classical fuzzy metric fixed-point theory
Summary
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