Approximation of Fractional-Order Operators

Reyad El-Khazali, Iqbal M. Batiha, Shaher Momani

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

24 Scopus citations

Abstract

In order to deal with some difficult problems in fractional-order systems, like computing analytical time responses such as unit impulse and step responses; some rational approximations for the fractional-order operators are presented with satisfying results in simulation and realization. In this chapter, several comparisons in the time response and Bode results between four well-known methods; Oustaloup’s method, Matsuda’s method, AbdelAty’s method, and El-Khazali’s method are made for the rational approximation of fractional-order operator (fractional Laplace operator). The various methods along with their advantages and limitations are described in this chapter. Simulation results are shown for different orders of the fractional operator. It has been shown in several numerical examples that the El-Khazali’s method is very successful in comparison with Oustaloup’s, Matsuda’s, and AbdelAty’s methods.

Original languageBritish English
Title of host publicationFractional Calculus - ICFDA 2018
EditorsPraveen Agarwal, Praveen Agarwal, Praveen Agarwal, Dumitru Baleanu, YangQuan Chen, Shaher Momani, José António Tenreiro Machado
PublisherSpringer
Pages121-151
Number of pages31
ISBN (Print)9789811504297
DOIs
StatePublished - 2019
EventInternational Conference on Fractional Differentiation and its Applications, ICFDA 2018 - Amman, Jordan
Duration: 16 Jul 201818 Jul 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume303
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Fractional Differentiation and its Applications, ICFDA 2018
Country/TerritoryJordan
CityAmman
Period16/07/1818/07/18

Keywords

  • AbdelAty’s approximation
  • El-Khazali’s approximation
  • Fractional-Order models
  • Matsuda’s approximation
  • Oustaloup’s approximation

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