Nonlinear Fractional Integrodifferential Equations via Fixed Point Theory in α , β ‐Extended Partial b ‐Metri

Generalized metric spaces provide a useful framework for studying fixed point problems in nonlinear equations when the standard metric structure is too restrictive. The two‐control formulation studied here allows pair‐dependent coefficients together with nonzero self‐distances. We clarify that its triangle inequality can be expressed using the single effective control θ = max{ α , β }; hence, the contribution is a parametrization and analysis of sufficient fixed point conditions. We establish fundamental structural and topological properties of the proposed space and develop several fixed point theorems under suitable contractive conditions. The applicability of the obtained results is demonstrated through a nonlinear fractional integrodifferential equation subject to nonlocal boundary conditions. In particular, the proposed framework provides sufficient conditions for the existence and uniqueness of solutions and offers a flexible setting for fixed point analysis of nonlinear fractional models. The results are compared with standard one‐control and Banach‐type conditions, and their limitations are stated explicitly.