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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Accuracy Assessment of Fractional Order Derivatives and Integrals Numerical Computations

Journal of Applied Nonlinear Dynamics 4(1) (2015) 53--65 | DOI:10.5890/JAND.2015.03.005

Dariusz W. Brzeziński; P.Ostalczyk

Institute of Applied Computer Science, Lodz University of Technology, 18/22 Stefanowskiego St., 90 -924 Łodź, Poland

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Abstract

This paper presents results of a numerical experiment, during which different numerical criteria of exact values setting in the accuracy assessment of fractional order derivatives / integrals numerical calculations are tested. Although traditional accuracy criteria in form of relative error expressed in % are applied, the values assumed as exact, necessary for comparison, are now: value of a function, classical 1st derivative, integral of the 1st order and Mittag-Leffler function’s values. For that purpose, fractional order differentiation and integration operators concatenation rules are applied. The methods allow to assess the accuracy of numerical calculations of fractional derivatives and integrals for each required function and not only for ones, for which mathematical formulas are available. The proposed measures are employed to determine proper operation and assess the accuracy of fractional order derivatives and integrals numerical algorithms.The algorithms utilize Riemann-Liouville and Grunwald-Letnikov frac-¨ tional order derivatives and integrals formulas.

Acknowledgments

The research is supported by the Polish National Science Center in 2013-2015 as a research project (DEC-2012/05/B/ST 6/03647).

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