Approximating fractional derivatives through the generalized mean

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

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

Original languageEnglish
Pages (from-to)3723-3730
Number of pages8
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number11
DOIs
Publication statusPublished - Nov 2009

Fingerprint

Fractional Derivative
Fractional Order
Discrete-time
Degree of freedom
Derivatives
Optimization
Demonstrate

Keywords

  • Average
  • Fractional calculus
  • Fractional derivatives
  • Generalized mean

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Approximating fractional derivatives through the generalized mean. / Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, J.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 11, 11.2009, p. 3723-3730.

Research output: Contribution to journalArticle

Tenreiro Machado, J. A. ; Galhano, Alexandra M. ; Oliveira, Anabela M. ; Tar, J. / Approximating fractional derivatives through the generalized mean. In: Communications in Nonlinear Science and Numerical Simulation. 2009 ; Vol. 14, No. 11. pp. 3723-3730.
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