Ortigueira, Manuel D.Machado, J. A. Tenreiro2021-12-072021-12-072020http://hdl.handle.net/10400.22/19020In 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.engDiscrete-timeFractional derivativeTime scaleBilinear transformationNew discrete-time fractional derivatives based on the bilinear transformation: Definitions and propertiesjournal article10.1016/j.jare.2020.02.011