Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Algoritmos genéticos: aplicação na síntese de alguns algoritmos de controlo

Mestrado em Engenharia Electrotécnica e de Computadores. Área de Especialização de Automação e Sistemas.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Enantiomeric fraction evaluation of pharmaceuticals in environmentalmatrices by liquid chromatography-tandem mass spectrometry

The interest for environmental fate assessment of chiral pharmaceuticals is increasing and enantioselective analytical methods are mandatory. This study presents an enantioselective analytical method for the quantification of seven pairs of enantiomers of pharmaceuticals and a pair of a metabolite. The selected chiral pharmaceuticals belong to three different therapeutic classes, namely selective serotonin reuptake inhibitors (venlafaxine, fluoxetine and its metabolite norfluoxetine), beta-blockers (alprenolol, bisoprolol, metoprolol, propranolol) and a beta2-adrenergic agonist (salbutamol). The analytical method was based on solid phase extraction followed by liquid chromatography tandem mass spectrometry with a triple quadrupole analyser. Briefly, Oasis® MCX cartridges were used to preconcentrate 250 mL of water samples and the reconstituted extracts were analysed with a Chirobiotic™ V under reversed mode. The effluent of a laboratory-scale aerobic granular sludge sequencing batch reactor (AGS-SBR) was used to validate the method. Linearity (r2 > 0.99), selectivity and sensitivity were achieved in the range of 20–400 ng L−1 for all enantiomers, except for norfluoxetine enantiomers which range covered 30–400 ng L−1. The method detection limits were between 0.65 and 11.5 ng L−1 and the method quantification limits were between 1.98 and 19.7 ng L−1. The identity of all enantiomers was confirmed using two MS/MS transitions and its ion ratios, according to European Commission Decision 2002/657/EC. This method was successfully applied to evaluate effluents of wastewater treatment plants (WWTP) in Portugal. Venlafaxine and fluoxetine were quantified as non-racemic mixtures (enantiomeric fraction ≠ 0.5). The enantioselective validated method was able to monitor chiral pharmaceuticals in WWTP effluents and has potential to assess the enantioselective biodegradation in bioreactors. Further application in environmental matrices as surface and estuarine waters can be exploited.

Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04