Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Design of CMOS Analog Integrated Fractional-Order CircuitsIntroduction

Design of CMOS Analog Integrated Fractional-Order Circuits: Introduction [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 dny/dxn, 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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Design of CMOS Analog Integrated Fractional-Order CircuitsIntroduction

Download PDF
11 pages

Loading next page...
 
/lp/springer-journals/design-of-cmos-analog-integrated-fractional-order-circuits-Yj0tBYU0HH
Publisher
Springer International Publishing
Copyright
© The Author(s) 2017
ISBN
978-3-319-55632-1
Pages
1 –12
DOI
10.1007/978-3-319-55633-8_1
Publisher site
See Chapter on Publisher Site

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 dny/dxn, 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.]

Published: Apr 13, 2017

Keywords: Fractional Derivative; Fractional Calculus; Continue Fraction Expansion; Electronic Tuning; Current Feedback Operational Amplifier

There are no references for this article.