Version 1
: Received: 12 September 2024 / Approved: 13 September 2024 / Online: 13 September 2024 (08:24:23 CEST)
How to cite:
West, B. Fractal Calculus Facilitates Rethinking 'Hard Problems'; A New Research Paradigm. Preprints2024, 2024091063. https://doi.org/10.20944/preprints202409.1063.v1
West, B. Fractal Calculus Facilitates Rethinking 'Hard Problems'; A New Research Paradigm. Preprints 2024, 2024091063. https://doi.org/10.20944/preprints202409.1063.v1
West, B. Fractal Calculus Facilitates Rethinking 'Hard Problems'; A New Research Paradigm. Preprints2024, 2024091063. https://doi.org/10.20944/preprints202409.1063.v1
APA Style
West, B. (2024). Fractal Calculus Facilitates Rethinking 'Hard Problems'; A New Research Paradigm. Preprints. https://doi.org/10.20944/preprints202409.1063.v1
Chicago/Turabian Style
West, B. 2024 "Fractal Calculus Facilitates Rethinking 'Hard Problems'; A New Research Paradigm" Preprints. https://doi.org/10.20944/preprints202409.1063.v1
Abstract
This paper intoduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the his- torical evolution of understaning an empirical medical process faciltated by the fractal calculus perspective. Herein we trace the analysis of the time series for heart rate varability (HRV) developed for diagnosing the cardiovascular health of a patient. This is done herein by introducing four (one empirical which en- tails three theoretical fractal models) distinct but related fractal models each one introduced to solve a particular problem arising from a fundamental defect in the previous model but in generalizing a model at one stage to resolve the problem associated with the defect another is invariably introduced by the re- placement model. It is through the utilization of the fractional calculus that the necessity for rethinking how to systematically incorporate additonal layers of complexity are revealed ultimately resulting in a 'complete' description of its empirical dynamics in fractal terms.
Keywords
Fractal Paradigm; fractal calculus; heart rate variability (HRV); Levy statistics; control hypothesis; sinoatrial node control
Subject
Biology and Life Sciences, Other
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
