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

Manuel D. Ortigueira, J. A. Tenreiro Machado

Research output: Contribution to journalReview articlepeer-review

5 Citations (Scopus)
6 Downloads (Pure)

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 languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Advanced Research
Volume25
DOIs
Publication statusPublished - Sep 2020

Keywords

  • bilinear transformation
  • Discrete-time
  • Fractional derivative
  • Time scale

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