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February 5, 20260 citationsOpen Access

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

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SİSİNAN İBAGÜNER

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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Cite This Study

SİNAN İBAGÜNER (2026) studied this question.

synapsesocial.com/papers/698434ebf1d9ada3c1fb3a01https://doi.org/10.13140/rg.2.2.17180.14725
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