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

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...

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Detalles Bibliográficos
Autores principales: Ortigueira, Manuel D., Tenreiro Machado, J.A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474201/
https://www.ncbi.nlm.nih.gov/pubmed/32922968
http://dx.doi.org/10.1016/j.jare.2020.02.011
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author Ortigueira, Manuel D.
Tenreiro Machado, J.A.
author_facet Ortigueira, Manuel D.
Tenreiro Machado, J.A.
author_sort Ortigueira, Manuel D.
collection PubMed
description 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.
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spelling pubmed-74742012020-09-11 New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties Ortigueira, Manuel D. Tenreiro Machado, J.A. J Adv Res Article 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. Elsevier 2020-02-25 /pmc/articles/PMC7474201/ /pubmed/32922968 http://dx.doi.org/10.1016/j.jare.2020.02.011 Text en © 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University. http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Article
Ortigueira, Manuel D.
Tenreiro Machado, J.A.
New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_full New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_fullStr New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_full_unstemmed New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_short New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
title_sort new discrete-time fractional derivatives based on the bilinear transformation: definitions and properties
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7474201/
https://www.ncbi.nlm.nih.gov/pubmed/32922968
http://dx.doi.org/10.1016/j.jare.2020.02.011
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