Noncommutative Fractal Dynamics in Anisotropic and Inhomogeneous Cosmologies

A composite entropy--weighted metric is constructed by integrating noncommutative and fractal corrections into the classical horizon entropy functional. Under boundedness and perturbative assumptions, the modified metric is shown to be well--posed, with its evolution remaining stable under small perturbations and its curvature invariants being regularized in regimes where classical divergences occur. In the homogeneous limit, the framework converges to the standard FLRW formulation.