New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

Manuel D. Ortigueira; J. A. Tenreiro Machado

doi:10.1016/j.jare.2020.02.011

New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

Manuel D. Ortigueira, J. A. Tenreiro Machado

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Abstract

In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Journal of Advanced Research
Volume	25
DOIs	https://doi.org/10.1016/j.jare.2020.02.011
Publication status	Published - Sept 2020

Keywords

bilinear transformation
Discrete-time
Fractional derivative
Time scale

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10.1016/j.jare.2020.02.011Licence: CC BY-NC-ND

New discrete-time fractional derivatives based on the bilinear transformation_Definitions and propertiesFinal published version, 822 KBLicence: CC BY-NC-ND

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AB - In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov derivatives. Their properties are described highlighting one important feature, namely that such derivatives have always long memory.

KW - bilinear transformation

KW - Discrete-time

KW - Fractional derivative

KW - Time scale

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New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties

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Keywords

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