Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

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.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Reactivity of human fetal and adult immortalized hepatocytes to potentially toxic bilirubin and bile acid species

Dissertação apresentada para a obtenção do Grau de Mestre em Genética Molecular e Biomedicina, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

SPE-LC-FD Determination of Polycyclic Aromatic Hydrocarbon Monohydroxy Derivatives in Cephalopods

A new analytical methodology, based on liquid chromatography with fluorescence detection (LC-FD), after extraction, enzymatic hydrolysis, and solid-phase extraction (SPE) through Oasis HLB cartridges, was developed and validated for the simultaneous determination of three monohydroxy derivatives of polycyclic aromatic hydrocarbons (PAHs). The optimized analytical method is sensitive, accurate, and precise, with recoveries between 62 and 110% and limits of detection of 227, 9, and 45 ng/g for 1-hydroxynaphthalene, 2-hydroxyfluorene, and 1-hydroxypyrene, respectively. Their levels were estimated in different cephalopod matrices (edible tissues and hemolymph). The methodology was applied to samples of the major cephalopod species consumed worldwide. Of the 18 samples analyzed, 39% were contaminated with 1-hydroxynaphthalene, which was the only PAH metabolite detected. Its concentration ranged from 786 to 1145 ng/g. This highly sensitive and specific method allows the identification and quantitation of PAH metabolites in forthcoming food safety and environmental monitoring programs.

Hydrogenating activity of Pt/zeolite catalysts focusing acid support and metal dispersion influence

Toluene hydrogenation was studied over catalysts based on Pt supported on large pore zeolites (HUSY and HBEA) with different metal/acid ratios. Acidity of zeolites was assessed by pyridine adsorption followed by FTIR showing only small changes before and after Pt introduction. Metal dispersion was determined by H2–O2 titration and verified by a linear correlation with the intensity of Pt0–CO band obtained by in situ FTIR. It was also observed that the electronic properties of Pt0 clusters were similar for the different catalysts. Catalytic tests showed rapid catalyst deactivation with an activity loss of 80–95% after 60 min of reaction. The turnover frequency of fresh catalysts depended both on metal dispersion and the support. For the same support, it changed by a 1.7-fold (HBEA) and 4.0-fold (HUSY) showing that toluene hydrogenation is structure-sensitive, i.e. hydrogenating activity is not a unique function of accessible metal. This was proposed to be due to the contribution to the overall activity of the hydrogenation of adsorbed toluene on acid sites via hydrogen spillover. Taking into account the role of zeolite acidity, the catalysts series were compared by the activity per total adsorbing sites which was observed to increase steadily with nPt/(nPt + nA). An increase of the accessible Pt atoms leads to an increase on the amount of spilled over hydrogen available in acid sites therefore increasing the overall activity. Pt/HBEA catalysts were found to be more active per total adsorbing site than Pt/HUSY which is proposed to be due to an augmentation in the efficiency of spilled over hydrogen diffusion related to the proximity between Pt clusters and acid sites. The intervention of Lewis acid sites in a greater extent than that measured by pyridine adsorption may also contribute to this higher activity of Pt/HBEA catalysts. These results reinforce the importance of model reactions as a closer perspective to the relevant catalyst properties in reaction conditions.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: Ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA = human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(eta(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy = bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(eta(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing. (C) 2015 Elsevier Inc All rights reserved.

Gastric acid secretion response in the Cebus apella: a monkey model of chronic Chagas disease

The objective was to study the secretory pattern, both basal and stimulated either by histamine (0.1 mg/kg) or pentagastrin (64 ug/kg) in eighteen Cebus apella monkeys chronically infected with different T. cruzi strains (CA1, n=10; Colombian, n=4 and Tulahuen, n=4) and to describe the morphological findings in the gastrointestinal tract in twelve infected (6 sacrificed and 6 spontaneously dead) and four healthy monkeys. All infected monkeys and 35 healthy ones were evaluated by contrast X-ray examination. No differences were observed in basal acid output between control and infected groups. Animals infected with the Tulahuen and Colombian strains showed significant lower values of peak acid output in response to histamine or pentagastrin (p<0.01 and p<0.05 respectively; "t" test) in comparison to the controls. Barium contrast studies showed enlargement and dilatation of the colon in three infected animals. Histopathological lesions were seen in 75% of the autopsied animals either in colon alone (33%) or both, in colon and esophagus (42%). The normal secretion observed in the CA1 infected group could be due to a lower virulence of the strain, a lower esophagic tropism or the necessity of a longer post-infection time to cause lesions.