Randomized trial demonstrates AI-based identification of fractional order in synthetic fractal signals, suggesting new methods for analyzing scaling laws.
Key Points
This paper aims to describe how fractional calculus transforms scaling structures and multifractal spectra systematically.
Establish a unified scaling-law theory integrating fractional operators and local regularity.
Derive transformation rules for structure-function scaling exponents and develop an AI-assisted identification framework.
Conduct numerical experiments on synthetic multifractal processes to validate theoretical predictions.
Fractional differentiation shifts local Hölder exponents, yielding an exact shift law for multifractal spectra.
An affine transformation rule for scaling exponents demonstrates linear deformations across statistical moments.
AI framework successfully recovers fractional orders from observed fractal signals with confirmed robustness.