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Fractional Calculus and Applied Analysis

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And I say to myself: “What a fractional world!”

J. Tenreiro Machado
  • Dept. of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal
  • Email:
Published Online: 2011-09-29 | DOI: https://doi.org/10.2478/s13540-011-0037-1


This paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

MSC: Primary 26A33; Secondary 60G22, 92B05, 92D20, 91G80, 86A15, 86A17, 86A10, 00A65

Keywords: fractional calculus; Fourier analysis; DNA; financial indices; earthquakes; global warming; music

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About the article

Published Online: 2011-09-29

Published in Print: 2011-12-01

Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-011-0037-1. Export Citation

© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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