What question did this study set out to answer?

The research seeks to introduce a new operator framework for modeling dynamics in systems with fractal structures and scale invariance.

February 5, 2026Open Access

Ibaguner Fractal Operator (IFO) Fractal Calculus: Surpassing Classical Newton-Leibniz Calculus by Being Scale-Invariant Singular Dynamics and Hyperbolic Renormalization

Puntos clave

The research seeks to introduce a new operator framework for modeling dynamics in systems with fractal structures and scale invariance.
Developed Ibaguner Fractal Operator (IFO) based on fractal measure spaces
Created scale-covariant kernels for modeling
Utilized hyperbolic renormalization maps to define dynamics
Demonstrated bounded compression dynamics on non-integer dimensional domains
Established scale-invariant evolution equations as a generalization of classical calculus
Classical calculus identified as a limiting case of the new framework

Resumen

Classical Newton-Leibniz calculus models dynamics on smooth manifolds with integer-dimensional measures and locally linear operators. Many natural and cosmological systems instead exhibit scale invariance, singular cores, and fractal microstructure. This paper introduces IFO Fractal Calculus, an operator framework built on fractal measure spaces, scale-covariant kernels, and hyperbolic renormalization maps. The Iba-guner Fractal Operator (IFO) defines bounded compression dynamics on non-integer dimensional domains and generates scale-invariant evolution equations. Classical calculus appears as a limiting special case. The framework provides a formal basis for singular-driven and fractal-scale dynamics.

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