Fractal-Stochastic Unified Model (MFSU) – Mathematical Derivation of the Core Equation - Version 1.0: Validated Core Equation

This document presents the mathematical derivation of the core equation of the Fractal-Stochastic Unified Model (MFSU), a theoretical framework designed to describe complex physical systems using fractional calculus, stochastic fields, and nonlinear dynamics. The derivation includes the use of fractional Laplacians, noise with Hurst exponent \( H \), and self-interaction terms. The critical fractional order \( \theta \approx 0.921 \) emerges as a unifying parameter validated across physical phenomena. This work presents **MFSU Version 1.0**, a validated and experimentally grounded formulation of the Unified Fractal-Stochastic Model. It supersedes the previous theoretical version available at [https://zenodo.org/records/15828185](https://zenodo.org/records/15828185), by deriving the final form of the equation and demonstrating its applicability through CMB simulations and empirical data. This version introduces the core equation: ∂ψ/∂t = α(−Δ)^α⁄2 ψ + β ξ_H(x,t)ψ − γψ³ + f(x,t) 📘 Note: The derivation is written in Spanish, but all equations are expressed in universal mathematical notation and remain fully understandable to the scientific community.