New discrete-time fractional derivatives based on the bilinear transformation: Definitions and properties
Manuel Duarte Ortigueira, J. A. Tenreiro Machado
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.
Topics & Concepts
Bilinear interpolationBilinear transformTransformation (genetics)Fractional calculusDiscrete time and continuous timeDerivative (finance)Applied mathematicsSimilarity (geometry)Computer scienceMathematicsStatisticsArtificial intelligenceChemistryEconomicsBiochemistryGeneFilter (signal processing)Financial economicsDigital filterComputer visionImage (mathematics)Fractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical SystemsAdvanced Control Systems Design