Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

J. A. Tenreiro Machado, Alexandra M. Galhano, Anabela M. Oliveira, J. Tar

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Original languageEnglish
Pages (from-to)482-490
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume15
Issue number3
DOIs
Publication statusPublished - Mar 2010

Fingerprint

Optimal Approximation
Fractional Derivative
Discrete-time
Genetic algorithms
Genetic Algorithm
Derivatives
Taylor series
Optimization
Flexibility
Evaluate
Approximation
Standards

Keywords

  • Fractional calculus
  • Fractional derivatives
  • Genetic algorithms
  • Optimization

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms. / Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, J.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 3, 03.2010, p. 482-490.

Research output: Contribution to journalArticle

Tenreiro Machado, J. A. ; Galhano, Alexandra M. ; Oliveira, Anabela M. ; Tar, J. / Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms. In: Communications in Nonlinear Science and Numerical Simulation. 2010 ; Vol. 15, No. 3. pp. 482-490.
@article{d46e4a4584cc477da806c60744906b90,
title = "Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms",
abstract = "This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Pad{\'e} expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.",
keywords = "Fractional calculus, Fractional derivatives, Genetic algorithms, Optimization",
author = "{Tenreiro Machado}, {J. A.} and Galhano, {Alexandra M.} and Oliveira, {Anabela M.} and J. Tar",
year = "2010",
month = "3",
doi = "10.1016/j.cnsns.2009.04.030",
language = "English",
volume = "15",
pages = "482--490",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

AU - Tenreiro Machado, J. A.

AU - Galhano, Alexandra M.

AU - Oliveira, Anabela M.

AU - Tar, J.

PY - 2010/3

Y1 - 2010/3

N2 - This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

AB - This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

KW - Fractional calculus

KW - Fractional derivatives

KW - Genetic algorithms

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=70349977336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349977336&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2009.04.030

DO - 10.1016/j.cnsns.2009.04.030

M3 - Article

VL - 15

SP - 482

EP - 490

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 3

ER -