Novel low-pass filter with adjustable parameters of~exponential-type forgetting

In this paper, a novel form of Gaussian filter, the Mittag-Leffler filter, is presented. This new filter uses a Mittag-Leffler function in the probability density function. Such Mittag-Leffler distribution is used in the convolution kernel of the filter. The filter has three parameters that may adjust the curve shape due to the filter forgetting factor. Illustrative examples present the main advantages of the proposed filter as compared to classical Gaussian filtering techniques. Some implementation notes, together with the Matlab function, are also presented.Comment: 5 pages, 6 figures, Matlab cod

State space description of national economies: the V4 countries

We present a new approach to description of national economies. For this we use the state space viewpoint, which is used mostly in the theory of dynamical systems and in the control theory. Gross domestic product, inflation, and unemployment rates are taken as state variables. We demonstrate that for the considered period of time the phase trajectory of each of the V4 countries (Slovak Republic, Czech Republic, Hungary, and Poland) lies approximately in one plane, so that the economic development of each country can be assocated with a corresponding plane in the state space. The suggested approach opens a way to a new set of economic indicators (for example, normal vectors of national economies, various plane slopes, 2D angles between the planes corresponding to different economies, etc.). The tool used for computations is orthogonal regression (alias orthogonal distance regression, alias total least squares method), and we also give general arguments for using orthogonal regression instead of the classical regression based on the least squares method. A MATLAB routine for fitting 3D data to lines and planes in 3D is provided.Comment: 13 pages, 18 figure

A fractional variational approach to the fractional basset-type equation

In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. We consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order. © 2013 Polish Scientific Publishers

On the mathematical properties of generalized fractional-order two-port networks using hybrid parameters

Linear passive and active electric circuits can be viewed as two-port networks -having two readily-accessible electrical terminals usually denoted as input and output ports. Two-port networks, also known as four-terminal networks, are usually represented using matrices which allow the network to be analyzed easily without getting through internal current and voltages. In this paper we present the mathematical properties of a generalized fractional-order two-port network represented as a symmetrical T-section through its hybrid parameters. © 2013 IEEE

Modelling heat transfer in heterogeneous media using fractional calculus

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Posicast control of a class of fractional-order processes

The number of studies on the control of fractional-order processes-processes having dynamics described by differential equations of arbitrary order-has been increasing in the past two decades and it is now ubiquitous. Various methods have emerged and have been proven to effectively control such processes-usually resulting in fractional-order controllers similar to their conventional integer-order counterparts, which include, but are not limited to fractional PID and fractional lead-lag controllers. However, such methods require a lot of computational effort and fractional-order controllers could be challenging when it comes to their synthesis and implementation. In this paper, we propose a simple yet effective delay-based controller with the use of the Posicast control methodology in controlling the overshoot of a fractional-order process of the class P: {P(s)=1(1asα + b)} having orders 1 \u3c α \u3c 2. Such controllers have proven to be easy to implement because they only require delays and summers. In this paper, the Posicast control methodology introduced in the past few years is modified to minimize the overshoot of the processes step response to a level that is acceptable in control engineering and automation practices. Furthermore, proof of the existence of overshoot for such class of processes, as well as the determination of the peak-time of the open-loop response of a fractional-order process of the class P is presented. Validation through numerical simulations for a class of fractional-order processes are presented in this paper. © 2013 Versita Warsaw and Springer-Verlag Wien