<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an improved second-order fractional differential equation operation method based on power series expansion. The algorithm's operation speed and accuracy performance are analyzed. The research found that the algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems.</p>
</abstract>

The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an improved second-order fractional differential equation operation method based on power series expansion. The algorithm's operation speed and accuracy performance are analyzed. The research found that the algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems.

Precision algorithms in second-order fractional differential equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Precision algorithms in second-order fractional differential equations"}

The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an...

Precision algorithms in second-order fractional differential equations

Online veröffentlicht: 30. Dez. 2021

Seitenbereich: 155 - 164

Eingereicht: 17. Juni 2021

Akzeptiert: 24. Sept. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00157

Schlüsselwörter
second-order fractional differential equation, fractional-order system, recursive algorithm, accuracy, power series expansion

© 2021 Chunguang Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Precision algorithms in second-order fractional differential equations

Online veröffentlicht: 30. Dez. 2021

Seitenbereich: 155 - 164

Eingereicht: 17. Juni 2021

Akzeptiert: 24. Sept. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00157

Schlüsselwörtersecond-order fractional differential equation, fractional-order system, recursive algorithm, accuracy, power series expansion

© 2021 Chunguang Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
second-order fractional differential equation, fractional-order system, recursive algorithm, accuracy, power series expansion