Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations via Common Fixed-Point Techniques in Complex Valued Fuzzy Metric Spaces

Abstract

The main purpose of this paper is to study the existence theorem for a common solution to a class of nonlinear three-point implicit boundary value problems of impulsive fractional differential equations. In this respect, we study the fuzzy version of some essential common fixed-point results from metric spaces in the newly introduced notion of complex valued fuzzy metric spaces. Also, we provide an illustrative example to demonstrate the validity of our derived results.

Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces

“…In the present era, significant research interest is directed towards exploring fixedpoint findings for mappings with complex-valued fuzzy metric approach. Prominent examples of such research include the works of [7,28] and the extensive investigations conducted by Humaira et al [12][13][14][15][16], which derived numerous relevance outcomes, along with practical applications. This manuscript presents a novel extension to the category of fuzzy metric spaces through introduction of complex-valued intuitionistic fuzzy metric spaces.…”