<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.</p></abstract>

In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.

Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations...

Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas

Publié en ligne: 01 janv. 2016

Pages: 23 - 44

Reçu: 01 juin 2015

Accepté: 04 nov. 2015

DOI: https://doi.org/10.21042/AMNS.2016.1.00003

© 2016 Dariusz W. Brzeziński, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.