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Erschienen in:
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2015 | OriginalPaper | Buchkapitel

1. Fractional Order Models

verfasst von : J. Sabatier, C. Farges, A. Oustaloup

Erschienen in: Fractional Order Differentiation and Robust Control Design

Verlag: Springer Netherlands

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Abstract

In a letter to L’Hospital in 1695, Leibniz raised the possibility of generalizing the operation of differentiation to non-integer orders and L’Hospital asked what would be the result of half-differentiating a variable. Leibniz in an open letter dated September 30, 1695 replied “It leads to a paradox, from which 1 day useful consequences will be drawn”. It was only at the beginning of the nineteenth century that the generalization of differentiation to real or complex orders was formalized with the work of Liouville and Riemann (Liouville 1832; Riemann 1876; Letnikov 1868). This generalization is referred to in the literature as “fractional calculus” (Oldham and Spanier 1974) but also as “fractional differentiation” or sometimes “generalized differentiation”. In this book, the terms “fractional differentiation” or “fractional integration” are used to describe fractional order differential operators. This denomination is the most prevalent, although it is restrictive as it subsumes under a single term differentiation orders that can be integer, fractional, real and/or complex.

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Nächstes Kapitel Fractional Order PID and First Generation CRONE Control System Design
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Metadaten
Titel
Fractional Order Models
verfasst von
J. Sabatier
C. Farges
A. Oustaloup
Copyright-Jahr
2015
Verlag
Springer Netherlands
Buch
Fractional Order Differentiation and Robust Control Design

Print ISBN: 978-94-017-9806-8

Electronic ISBN: 978-94-017-9807-5

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-94-017-9807-5_1

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