Efficient Fixed-Point Method with Application to a Fractional Blood Flow Model

This paper introduces two generalized frameworks, the extended bipolar parametric b-metricspace (EBPbMS) and the extended bipolar fuzzy b-metric space (EBFbMS), which unify and extend several existing bipolar and fuzzy metric structures. Within these settings, new fixed-point results are established for covariant and contravariant Meir–Keeler-type contractions. A fundamental correspondence between EBFbMSs and EBPbMSs is developed, providing a unified basis for analyzing convergence and stability in generalized metric environments. An illustrative example and an application to a fractional blood flow model confirm the effectiveness of the proposed approach and ensure the existence and uniqueness of the solution. These results demonstrate the capability of extended bipolar structures to model nonlinear fractional systems with memory effects.