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Erschienen in:
Buchtitelbild

2017 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : Georgia Tsirimokou, Costas Psychalinos, Ahmed Elwakil

Erschienen in: Design of CMOS Analog Integrated Fractional-Order Circuits

Verlag: Springer International Publishing

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Abstract

Fractional calculus is three centuries old as the conventional calculus and consist a super set of integer-order calculus, which has the potential to accomplish what integer-order calculus cannot. Its origins dating back to a correspondence from 1695 between Leibnitz and L’Hôpital, with L’Hôpital inquiring about Leibnitz notation for the n-th derivative of a function d n y/dx n , i.e. what would be the result if n = 1/2. The reply from Leibnitz, “It will lead to a paradox, a paradox from which one day useful consequences will be drawn, because there are no useless paradoxes”, was the motivation for fractional calculus to be born. Fractional calculus does not mean the calculus of fractions, nor does it mean a fraction of any calculus differentiation, integration or calculus of variations. The fractional calculus is a name of theory of integrations and derivatives of arbitrary order, which unify and generalize the notation of integer-order differentiation and n-fold integration. The beauty of this subject is that fractional derivatives and integrals translate better the reality of nature! This feature turns it into an efficient tool, offering the capability of having available a language of nature, which can be used to talk with.

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Nächstes Kapitel Procedure for Designing Fractional-Order Filters
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Metadaten
Titel
Introduction
verfasst von
Georgia Tsirimokou
Costas Psychalinos
Ahmed Elwakil
Copyright-Jahr
2017
Buch
Design of CMOS Analog Integrated Fractional-Order Circuits

Print ISBN: 978-3-319-55632-1

Electronic ISBN: 978-3-319-55633-8

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-55633-8_1

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