Application of integer and fractional models in electrochemical systems

This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.

Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

Fractional calculus: a survey of useful formulas

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.

Science metrics on fractional calculus development since 1966

During the last fifty years the area of Fractional Calculus verified a considerable progress. This paper analyzes and measures the evolution that occurred since 1966.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

On the implementation of real-time slotbased task-splitting scheduling algorithms for multiprocessor systems

In this paper we discuss challenges and design principles of an implementation of slot-based tasksplitting algorithms into the Linux 2.6.34 version. We show that this kernel version is provided with the required features for implementing such scheduling algorithms. We show that the real behavior of the scheduling algorithm is very close to the theoretical. We run and discuss experiments on 4-core and 24-core machines.

Implementing multicore real-time scheduling algorithms based on task splitting using ada 2012

Multiprocessors, particularly in the form of multicores, are becoming standard building blocks for executing reliable software. But their use for applications with hard real-time requirements is non-trivial. Well-known realtime scheduling algorithms in the uniprocessor context (Rate-Monotonic [1] or Earliest-Deadline-First [1]) do not perform well on multiprocessors. For this reason the scientific community in the area of real-time systems has produced new algorithms specifically for multiprocessors. In the meanwhile, a proposal [2] exists for extending the Ada language with new basic constructs which can be used for implementing new algorithms for real-time scheduling; the family of task splitting algorithms is one of them which was emphasized in the proposal [2]. Consequently, assessing whether existing task splitting multiprocessor scheduling algorithms can be implemented with these constructs is paramount. In this paper we present a list of state-of-art task-splitting multiprocessor scheduling algorithms and, for each of them, we present detailed Ada code that uses the new constructs.

An introduction to the fractional continuous-time linear systems

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

On the fractional central differences and derivatives

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

Control of baker’s yeast fermentation: PID and fuzzy algorithms

A MATLAB/SIMULINK-based simulator was employed for studies concerning the control of baker’s yeast fed-batch fermentation. Four control algorithms were implemented and compared: the classical PID control, two discrete versions- modified velocity and position algorithms, and a fuzzy law. The simulation package was seen to be an efficient tool for the simulation and tests of control strategies of the nonlinear process.