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

J Adv Res. 2020 Feb 25:25:1-10. doi: 10.1016/j.jare.2020.02.011. eCollection 2020 Sep.

Authors

Manuel D Ortigueira¹, J A Tenreiro Machado²

Affiliations

¹ CTS-UNINOVA and NOVA Faculty of Sciences and Technology of Nova University of Lisbon, Campus da FCT da UNL, Quinta da Torre, 2829 - 516 Caparica, Portugal.
² Institute of Engineering, Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal.

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.

Keywords: Discrete-time; Fractional derivative; Time scale; bilinear transformation.

Publication types

Review