<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Numerical computation of fractional order derivatives and integrals can be done by applying many approaches. They include Riemann-Liouville and Caputo formulas. Both formulas include fractional order integration and integer order differentiation but in a different order: fractional order integration can be preceded by integer order differentiation or it can be done in the reverse order. In the paper we apply both formulas for FOD computation and investigate if an application of a particular order have any advantages, e.g. resulting in higher accuracy. The outcome of the experiment is that by applying adequately selected formula of FOD computation according to the shape of a particular function, the accuracy of computation can often be increased. Application of Riemann-Liouville formula enables successful FOD computation for functions which <italic>n<sup>th</sup></italic> derivative does not exist.</p></abstract>

Numerical computation of fractional order derivatives and integrals can be done by applying many approaches. They include Riemann-Liouville and Caputo formulas. Both formulas include fractional order integration and integer order differentiation but in a different order: fractional order integration can be preceded by integer order differentiation or it can be done in the reverse order. In the paper we apply both formulas for FOD computation and investigate if an application of a particular order have any advantages, e.g. resulting in higher accuracy. The outcome of the experiment is that by applying adequately selected formula of FOD computation according to the shape of a particular function, the accuracy of computation can often be increased. Application of Riemann-Liouville formula enables successful FOD computation for functions which nth derivative does not exist.

Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition

Applied Mathematics and Nonlinear Sciences

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

Numerical computation of fractional order derivatives and integrals can be done by applying many approaches. They include Riemann-Liouville and Caputo...

Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition

Published Online: Jun 25, 2017

Page range: 237 - 248

Received: Jan 18, 2017

Accepted: Jun 25, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00020

Keywords
Accuracy of computation, Numerical Fractional Order Differentiation, Integration

© 2017 Dariusz W. Brzeziński, published by Sciendo

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

Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition

Published Online: Jun 25, 2017

Page range: 237 - 248

Received: Jan 18, 2017

Accepted: Jun 25, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00020

KeywordsAccuracy of computation, Numerical Fractional Order Differentiation, Integration

© 2017 Dariusz W. Brzeziński, published by Sciendo

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

Keywords
Accuracy of computation, Numerical Fractional Order Differentiation, Integration