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Search results for: Fractional generalization
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublicationRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Darboux covariant equations of von Neumann type and their generalization.
PublicationOpisano nową klasę uogólnionych równań von Neumanna całkowalnych przez transformację Darboux. Uogólnienie zawiera jako przypadki szczególne nieliniowe równanie von Neumanna, r. Nahma, kratę Tody i inne.
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Learning from examples with data reduction and stacked generalization
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An approach to machine classification based on stacked generalization and instance selection
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Generalization of Phylogenetic Matching Metrics with Experimental Tests of Practical Advantages
PublicationThe ability to quantify a dissimilarity of different phylogenetic trees is required in various types of phylogenetic studies, for example, such metrics are used to assess the quality of phylogeny construction methods and to define optimization criteria in supertree building algorithms. In this article, starting from the already described concept of matching metrics, we define three new metrics for rooted phylogenetic trees. One...
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Generalization of the elastic network model for the study of large conformational changes in biomolecules
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Generalization of the Elastic Network Model for the Study of Large Conformational Changes in Proteins
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Developing a model of cooperation between universities and business - the generalization of cases of cooperation
PublicationThe aim of this paper is to present a model of cooperation between universities and business.
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Digital Cartographic Generalization – Study of Its Thresholds and Stages in Example of Cartographic Line
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Thermostatistics based on Kolmogorov-Nagumo averages: unifying frameworkfor extensive and nonextensive generalizations
PublicationUogólnienie formalizmu termostatyki przy pomocy średnich Kołmogorowa-Nagumo.
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Reduction of measurement data before Digital Terrain Model generation vs. DTM generalisation
PublicationModern data acquisition technologies provide large datasets that are not always necessary in its entirety to properly accomplish the goal of the study. In addition, such datasets are often cumbersome for rational processing, and their processing is time and labour consuming. Therefore, methods that enable to reduce the size of the measurement dataset, such as the generalization of the Digital Terrain Model (DTM) or the reduction...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublicationIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublicationA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...
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A Note on Fractional Curl Operator
PublicationIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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A Nyquist filter of fractional delay
PublicationIn the paper a novel discrete-time FIR fractonal delay specjal filter is investigated. This is a Nyquist filter which, besides the traditional its attribute (interymbol interference (ISI) free property), has the ability to compensate for subsample transmission delay involved, for example, in multipath propagation channel. The performance of the filter is analysed and illustrated.
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Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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Fractional differential equations with causal operators
PublicationWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Some applications of fractional order calculus
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Fractional Order Models of Dynamic Systems
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Optimal Control for Discrete Fractional Systems
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Fractional Order Dynamic Positioning Controller
PublicationImproving the performance of Dynamic Positioning System in such applications as station keeping, position mooring and slow speed references tracking requires improving the position and heading control precision. These goals can be achieved through the improvement of the ship control system. Fractional-order calculus is a very useful tool which extends classical, integer-order calculus and is used in contemporary modeling and control...
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Fractional differential equations with deviating arguments
PublicationDla równań różniczkowych typu ułamkowego, zostały podane warunki dostateczne na istnienie jednego rozwiązania lub rozwiazań ekstremalnych. Nierówności różniczkowe są też doskutowane.
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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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On Applications of Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Fractional Derivatives Application to Image Fusion Problems
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Electromagnetic-based derivation of fractional-order circuit theory
PublicationIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublicationModern regulators of synchronous generators, including voltage regulators, are digital systems, in their vast majority with standard structures contained in the IEEE standard. These are systems described with stationary differential equations of integral order. Differential equations of fractional order are not employed in regulators for synchronous generator control. This paper presents an analysis of the possibilities of using...
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Stability of Discrete Fractional Order State-space Systems
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Comparison and validation of integer and fractional order ultracapacitor models
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Time domain validation of ultracapacitor fractional order model
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Diffusion process modeling by using fractional-order models
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A complex variable fractional-delay FIR filter structure
PublicationW artykule wprowadzamy strukturę zespolonego filtru o skończonej odpowiedzi impulsowej (ang. finite impulse response - FIR) ze zmiennym opóźnieniem ułamkowym (ang. fractional delay - FD). Strukturę tę otrzymujemy na podstawie przestrajanego filtru FD FIR o współczynnikach rzeczywistych. Stanowi ona połączenie zbioru liniowo-fazowych filtrów FIR o współczynnikach stałych rzeczywistych i dwóch łańcuchów mnożąco-akumulujących, zawierających...
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Fractional Delay Filter Design for Sample Rate Conversion
PublicationRosnąca liczba różnych standardów szybkości próbkowania stwarza potrzebę stosowania algorytmów konwersji szybkości próbkowania ciągów dyskretnych. Jeżeli współczynnik przepróbkowania nie jest wyrażony jako stosunek małych liczb całkowitych albo gdy nie jest on stały, to rozwiązaniem może być użycie filtrów ułamkowoopóźniających. Umożliwiają one realizację przepróbkowania z dowolną krotnością. Dokładność przepróbkowania algorytmów...
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Fractional Delay Filter Design with Extracted Window Offsetting
PublicationW pracy przedstawiono koncepcję projektowania filtrów ułamkowoopóźniających (FD) bazującą na metodzie okien. W zaproponowanym podejściu w projektowaniu jest używane okno wyodrębnione z odpowiedzi impulsowej filtru optymalnego offsetowanego o opóźnienie ułamkowe projektowanego filtru. Poszczególne filtry FD zaprojektowany w ten sposób nie są optymalnymi filtrami FD, jednak oferują lepszą jakość w zastosowaniu do zmiany szybkości...
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Square root RC Nyquist filter of fractional delay
PublicationIn this paper we propose a discrete-time FIR (finite impulse response) filter which couples the role of square root Nyquist filter with fractional delay filter. This filter enables to substitute for a cascade of square root RC (SRRC) Nyquist filter and fractional delay filter in one device/algorithm. The aim is to compensate for transmission delay in communication system. Statistically defined performances, e.g. BER (bit error...
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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Functional differential equations
PublicationSformułowano dość ogólne warunki dostateczne na to, aby odpowiednio zdefiniowane ciągi monotoniczne były zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia początkowego dla funkcyjnych równań różniczkowych. Omawiane równanie jest ogólne, a np. zwyczajne równania różniczkowe czy równania różniczkowo-całkowe są jego szczególnymi przypadkami.
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Amino-modified mesoporous silica SBA-15 as bifunctional drug delivery system for cefazolin: Release profile and mineralization potential
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Aminopropyl-functionalized mesoporous silica SBA-15 as drug carrier for cefazolin: adsorption profiles, release studies, and mineralization potential
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Thermally activated persulfate-based Advanced Oxidation Processes — recent progress and challenges in mineralization of persistent organic chemicals: a review
PublicationThermally activated persulfate (TAP) finds application in Advanced Oxidation Processes for the removal of pollutants from contaminated water and soil. This paper reviewed the various cases of TAP in the environmental remediation. The pollutants such as individual pharmaceuticals, biocides, cyclic organic compounds, and dyes are considered in this review. It is interesting to note that most of the organic compounds undergo complete...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Frequency response based identification of fractional order dynamical systems
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