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.

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.

Multidimensional scaling analysis of fractional systems

This paper investigates the use of multidimensional scaling in the evaluation of fractional system. Several algorithms are analysed based on the time response of the closed loop system under the action of a reference step input signal. Two alternative performance indices, based on the time and frequency domains, are tested. The numerical experiments demonstrate the feasibility of the proposed visualization method.

Introducing the fractional-order Darwinian PSO

One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machinelearning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

Hybrid adaptive control of a dragonfly model

Dragonflies show unique and superior flight performances than most of other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper, it is presented an adaptive scheme controlling a nonlinear model inspired in a dragonfly-like robot. It is proposed a hybrid adaptive (HA) law for adjusting the parameters analyzing the tracking error. At the current stage of the project it is considered essential the development of computational simulation models based in the dynamics to test whether strategies or algorithms of control, parts of the system (such as different wing configurations, tail) as well as the complete system. The performance analysis proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence.

A simulation model for the IEEE 802.15.4 protocol: delay/throughput evaluation of the GTS mechanism

The IEEE 802.15.4 protocol has the ability to support time-sensitive Wireless Sensor Network (WSN) applications due to the Guaranteed Time Slot (GTS) Medium Access Control mechanism. Recently, several analytical and simulation models of the IEEE 802.15.4 protocol have been proposed. Nevertheless, currently available simulation models for this protocol are both inaccurate and incomplete, and in particular they do not support the GTS mechanism. In this paper, we propose an accurate OPNET simulation model, with focus on the implementation of the GTS mechanism. The motivation that has driven this work is the validation of the Network Calculus based analytical model of the GTS mechanism that has been previously proposed and to compare the performance evaluation of the protocol as given by the two alternative approaches. Therefore, in this paper we contribute an accurate OPNET model for the IEEE 802.15.4 protocol. Additionally, and probably more importantly, based on the simulation model we propose a novel methodology to tune the protocol parameters such that a better performance of the protocol can be guaranteed, both concerning maximizing the throughput of the allocated GTS as well as concerning minimizing frame delay.

A lightweight indoor localization model based on motley-keenan and COST

This paper presents a novel approach to WLAN propagation models for use in indoor localization. The major goal of this work is to eliminate the need for in situ data collection to generate the Fingerprinting map, instead, it is generated by using analytical propagation models such as: COST Multi-Wall, COST 231 average wall and Motley- Keenan. As Location Estimation Algorithms kNN (K-Nearest Neighbour) and WkNN (Weighted K-Nearest Neighbour) were used to determine the accuracy of the proposed technique. This work is based on analytical and measurement tools to determine which path loss propagation models are better for location estimation applications, based on Receive Signal Strength Indicator (RSSI).This study presents different proposals for choosing the most appropriate values for the models parameters, like obstacles attenuation and coefficients. Some adjustments to these models, particularly to Motley-Keenan, considering the thickness of walls, are proposed. The best found solution is based on the adjusted Motley-Keenan and COST models that allows to obtain the propagation loss estimation for several environments.Results obtained from two testing scenarios showed the reliability of the adjustments, providing smaller errors in the measured values values in comparison with the predicted values.

A sensitivity study of the WRF model in wind simulation for an area of high wind energy

The performance of the Weather Research and Forecast (WRF) model in wind simulation was evaluated under different numerical and physical options for an area of Portugal, located in complex terrain and characterized by its significant wind energy resource. The grid nudging and integration time of the simulations were the tested numerical options. Since the goal is to simulate the near-surface wind, the physical parameterization schemes regarding the boundary layer were the ones under evaluation. Also, the influences of the local terrain complexity and simulation domain resolution on the model results were also studied. Data from three wind measuring stations located within the chosen area were compared with the model results, in terms of Root Mean Square Error, Standard Deviation Error and Bias. Wind speed histograms, occurrences and energy wind roses were also used for model evaluation. Globally, the model accurately reproduced the local wind regime, despite a significant underestimation of the wind speed. The wind direction is reasonably simulated by the model especially in wind regimes where there is a clear dominant sector, but in the presence of low wind speeds the characterization of the wind direction (observed and simulated) is very subjective and led to higher deviations between simulations and observations. Within the tested options, results show that the use of grid nudging in simulations that should not exceed an integration time of 2 days is the best numerical configuration, and the parameterization set composed by the physical schemes MM5–Yonsei University–Noah are the most suitable for this site. Results were poorer in sites with higher terrain complexity, mainly due to limitations of the terrain data supplied to the model. The increase of the simulation domain resolution alone is not enough to significantly improve the model performance. Results suggest that error minimization in the wind simulation can be achieved by testing and choosing a suitable numerical and physical configuration for the region of interest together with the use of high resolution terrain data, if available.

Supplier's selection model based on an empirical study

The problem of selecting suppliers/partners is a crucial and important part in the process of decision making for companies that intend to perform competitively in their area of activity. The selection of supplier/partner is a time and resource-consuming task that involves data collection and a careful analysis of the factors that can positively or negatively influence the choice. Nevertheless it is a critical process that affects significantly the operational performance of each company. In this work, there were identified five broad selection criteria: Quality, Financial, Synergies, Cost, and Production System. Within these criteria, it was also included five sub-criteria. After the identification criteria, a survey was elaborated and companies were contacted in order to understand which factors have more weight in their decisions to choose the partners. Interpreted the results and processed the data, it was adopted a model of linear weighting to reflect the importance of each factor. The model has a hierarchical structure and can be applied with the Analytic Hierarchy Process (AHP) method or Value Analysis. The goal of the paper it's to supply a selection reference model that can represent an orientation/pattern for a decision making on the suppliers/partners selection process

Time-delay and fractional derivatives

This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based on the Fourier analysis an approximation of fractional derivatives through timedelayed samples is developed. Furthermore, the parameters of the proposed approximation are estimated by means of genetic algorithms. The results demonstrate the feasibility of the new perspective.

Fractional dynamics in liquid manipulation

This paper presents a fractional calculus perspective in the study of signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs off-line and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system and the trajectory planning to be used in reducing or eliminating the effect of vibrations.

Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Exploiting sensor redundancy for the calculation of fractional derivatives in the presence of noise

In this paper a new method for the calculation of the fractional expressions in the presence of sensor redundancy and noise, is presented. An algorithm, taking advantage of the signal characteristics and the sensor redundancy, is tuned and optimized through genetic algorithms. The results demonstrate the good performance for different types of expressions and distinct levels of noise.