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 order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Mots(dits) écrits:formes et valeurs de la diffusion des idées au 18ème siècle, au Portugal

Les rapports complexes entre les différentes façons de faire circuler les idées et les informations ne datent pas de nos jours. A toutes les époques, les messages qui circulent emploient toutes sortes de véhicules et de langages, très souvent complémentaires. Ces véhicules et ces langages n'ont peut-être rien d'extraordinaire. Ils appartiennent au monde des gestes de tous les jours, des gestes qui se répètent et dont la répétition est elle-même importante pour la construction du sens de chaque message. Ces gestes qui sont répétés, qui sont attendus et qui sont reconnus incluent des sons, des images, des comportements, des mots, ou des citations. Il y a donc un rapport qui s'y établit entre répétition et nouveauté, rapport dans lequel la répétition fournit chaque fois une nouvelle information, même si elle est déjà attendue, tandis que leur absence peut représenter l'anxiété, ou même le scandale.

New insights into pseudo-fractional ARMA modelling

Proceedings of the International Conference on Computational Cybernetics, Vienna University of Technology, August 30 - September 1, 2004

Fractional central differences and derivatives

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

Diffusion and efficiency of ISO 9001 in Portugal: a qualitative and quantitative study from a holistic theoretical perspective

Purpose – the aim of this paper is to analyse the diffusion and efficiency of ISO 9001 on different sectors of activity Design/methodology/approach – for that purpose, a holistic an integrative theoretical approach was based on the scope of the Contingency theory, the Institutional theory and the Resources-Based View (RBV). This theorethical perspective was used in a broad empirical study, using a qualitative and quantitative methodology, concerning Portuguese companies from different sectors of activity. Findings – according to the findings from both perspectives, a ranked combination of the named theoretical frame was constructed. Research limitations/implications – as to the analysis of the efficiency of ISO 9000, one of the limitations of this study lays in the consideration of just two sectors of activity, and another relates to its domestic geographical placement. Practical implications – this study used the ISO 9001 structure for the interviews and this has revealed very useful for the organizations to grasp the matters inquired. Originality/value – a relevant contribution to the state of art is achieved through the considered theoretical scope of analysis

Comparison of contaminant removal effectiveness and air change efficiency as indicator of air diffusion quality.

The ventilation efficiency concept is an attempt to quantify a parameter that can easily distinguish the different options for air diffusion in the building spaces. Thirteen strategies of air diffusion were measured in a test chamber through the application of the tracer gas method, with the objective to validate the calculation by Computational fluid dynamics (CFD). Were compared the Air Change Efficiency (ACE) and the Contaminant Removal Effectiveness (CRE), the two indicators most internationally accepted. The main results from this work shows that the values of the numerical simulations are in good agreement with experimental measurements and also, that the solutions to be adopted for maximizing the ventilation efficiency should be the schemes that operate with low speeds of supply air and small differences between supply air temperature and the room temperature.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Laser-induced diffusion decomposition in Fe-V thin-film alloys

We investigate the origin of ferromagnetism induced in thin-film (similar to 20 nm) Fe-V alloys by their irradiation with subpicosecond laser pulses. We find with Rutherford backscattering that the magnetic modifications follow a thermally stimulated process of diffusion decomposition, with formation of a-few-nm-thick Fe enriched layer inside the film. Surprisingly, similar transformations in the samples were also found after their long-time (similar to 10(3) s) thermal annealing. However, the laser action provides much higher diffusion coefficients (similar to 4 orders of magnitude) than those obtained under standard heat treatments. We get a hint that this ultrafast diffusion decomposition occurs in the metallic glassy state achievable in laser-quenched samples. This vitrification is thought to be a prerequisite for the laser-induced onset of ferromagnetism that we observe. 2014 Elsevier B.V. All rights reserved.

A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.