Applications of \(\mathcal{C}_{G}\)-class mappings with \(\mathscr{F}_{G}(\varphi, \wp, \varpi)\)-cyclic coupled rational contractions in partial b-metric spaces

Abstract

The primary goal of this research is to derive generalized \(\mathcal{C}_{\mathit{G}}\)-class functions and prove that a common coupled fixed point exists for \(\mathscr{F}_{\mathit{G}}(\varphi, \wp, \varpi)\)-cyclic rational contraction in partial b-metric spaces(PbMS). In our study, we use some properties of different control functions. Our findings broaden and unify a number of previous results in the literature. The conclusions are supported by examples. In addition, we provide applications for integral equations and homotopy as well as an explanation of the significance of the obtained results.