Unified Fractal Dynamics (UFD) – Foundations and Fractal Spacetime (Combined Parts 1 & 2)

This merged paper consolidates the first two parts of the Unified Fractal Dynamics (UFD) series, providing a comprehensive foundation and explicit derivation of fractal field equations. It establishes a covariant framework of fractal-dynamical spacetime, introducing the dynamical fractal dimension field , fractal metrics, and fractal derivatives, unifying gravity, gauge fields, and matter. Key contributions include: Definition and properties of fractal metrics and derivatives Construction of the unified action combining gravitational, scalar, gauge, and matter sectors Derivation of fractal Christoffel symbols, Riemann and Ricci tensors Explicit fractal Einstein field equations and energy-momentum tensors Fractal Yang–Mills and Dirac equations for matter fields Illustrative solutions in cosmology and spherically symmetric black hole spacetimes This paper provides the foundational basis for subsequent UFD parts, enabling a consistent extension toward renormalization, dimensional flow, black hole dynamics, and the complete Theory of Everything.