This paper extends IFO Fractal Calculus by linking its operator structure to fractal spacetime regimes and fractal eigenbasis theory. Dimension-dependent Hausdorff measures are incorporated into IFO dynamics, yielding spectral and evolution laws tied to cosmological and singularity regimes. Big Bang and black hole states are modeled as distinct fractal-dimension phases governed by hyperbolic compression operators. A fractal eigenbasis representation theorem is established, providing a scale-adaptive decomposition of fields.
SİNAN İBAGÜNER (Thu,) studied this question.