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

Ortigueira, Manuel D.Tenreiro Machado, J. A.2021-03-192021-03-192020-092090-1232PURE: 28463628PURE UUID: ead3e6fd-a4ed-4eb0-93e8-54e926e3b4c1Scopus: 85082812302PubMed: 32922968PubMedCentral: PMC7474201WOS: 000568361200001http://hdl.handle.net/10362/114148UIDB/00066/2020In 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.10841378engbilinear transformationDiscrete-timeFractional derivativeTime scaleGeneralNew discrete-time fractional derivatives based on the bilinear transformation: Definitions and propertiesreview10.1016/j.jare.2020.02.011https://www.scopus.com/pages/publications/85082812302