What question did this study set out to answer?

The aim is to connect fractal calculus with spacetime through eigenbasis theory and Hausdorff measures.

February 5, 2026Open Access

Ibaguner Fractal Operator : IFO Fractal Calculus II: Fractal Eigenbasis and Dimension-Dependent Spacetime Regimes

Key Points

The aim is to connect fractal calculus with spacetime through eigenbasis theory and Hausdorff measures.
Developed a fractal eigenbasis representation theorem.
Incorporated dimension-dependent Hausdorff measures into IFO dynamics.
Modeled Big Bang and black hole states using hyperbolic compression operators.
Established links between IFO dynamics and spectral laws in cosmological regimes.
Identified distinct fractal-dimension phases for different spacetime conditions.
Provided a scale-adaptive decomposition for fields in fractal dynamics.

Abstract

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.

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SİNAN İBAGÜNER

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Ibaguner Fractal Operator : IFO Fractal Calculus II: Fractal Eigenbasis and Dimension-Dependent Spacetime Regimes

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Abstract

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