Fractional calculus in bioengineering, part 2

Critical Reviews in Biomedical Engineering
Richard L Magin

Abstract

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane...Continue Reading

Citations

Apr 3, 2009·Journal of Pharmacokinetics and Pharmacodynamics·Aristides Dokoumetzidis, Panos Macheras
May 11, 2010·Journal of Pharmacokinetics and Pharmacodynamics·Davide Verotta
Apr 12, 2013·PloS One·Zoran B VosikaJovana B Simic-Krstic
Oct 15, 2014·IEEE Transactions on Neural Networks and Learning Systems·Yi-Fei PuPatrick Siarry
Sep 14, 2013·Computer Methods and Programs in Biomedicine·Saptarshi Das, Koushik Maharatna
Jan 3, 2012·Journal of Biological Physics·Guy Richard Kol, Paul Woafo
Aug 5, 2008·Physics in Medicine and Biology·Damian CraiemGustavo V Guinea
Jan 15, 2014·Annals of Biomedical Engineering·Paris Perdikaris, George Em Karniadakis
Oct 11, 2011·Clinical Physiology and Functional Imaging·Naser AhmadiMatthew Budoff
Jan 1, 2013·Mathematical Modelling of Natural Phenomena·Mark M Meerschaert, Peter Straka
Mar 24, 2020·Proceedings. Mathematical, Physical, and Engineering Sciences·Sansit PatnaikFabio Semperlotti
Aug 9, 2020·Scientific Reports·Yu M EfremovP S Timashev

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