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Introduction

  • Georgia Tsirimokou
  • Costas Psychalinos
  • Ahmed Elwakil
Chapter
  • 565 Downloads
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

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.

Keywords

Fractional Derivative Fractional Calculus Continue Fraction Expansion Electronic Tuning Current Feedback Operational Amplifier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Georgia Tsirimokou
    • 1
  • Costas Psychalinos
    • 1
  • Ahmed Elwakil
    • 2
    • 3
  1. 1.Physics Department Electronics LaboratoryUniversity of PatrasRio PatrasGreece
  2. 2.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityCairoEgypt

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