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Wyniki wyszukiwania dla: fractional derivations
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Functional delay fractional equations
PublikacjaIn 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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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublikacjaIn 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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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn 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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On Applications of Fractional Derivatives in Circuit Theory
PublikacjaIn 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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Fractional Derivatives Application to Image Fusion Problems
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Electromagnetic-based derivation of fractional-order circuit theory
PublikacjaIn 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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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublikacjaIn 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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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublikacjaStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Extracting functional groups of ALLINI to design derivatives of FDA‐approved drugs: Inhibition of HIV‐1 integrase
PublikacjaHIV‐1 integrase (IN) is crucial for integration of viral DNA into the host genome and a promising target in development of antiretroviral inhibitors. In this work, six new compounds were designed by linking the structures of two different class of HIV‐1 IN inhibitors (active site binders and allosteric IN inhibitors (ALLINIs)). Among newly designed compounds, INRAT10b was found most potent HIV‐1 IN inhibitor considering different...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublikacjaIn 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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Density Functional Theory Studies on Ir Spectra of the Triphenylene Derivatives. A Scaled Quantum Mechanical Force Field Approach
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublikacjaA 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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Fractional problems with advanced arguments
PublikacjaThis 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
PublikacjaIn 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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A Note on Fractional Curl Operator
PublikacjaIn 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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IR–Raman, NMR and density functional methods in the examination of tautomerism and features of N-methyl substituted 9-acridinamine derivatives
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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 differential equations with deviating arguments
PublikacjaDla 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
PublikacjaIn 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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Fractional differential equations with causal operators
PublikacjaWe 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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Fractional Order Dynamic Positioning Controller
PublikacjaImproving 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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Systems of Nonlinear Fractional Differential Equations
PublikacjaUsing 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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Fundamental properties of solutions to fractional-order Maxwell's equations
PublikacjaIn 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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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
PublikacjaW 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 Order Circuit Elements Derived from Electromagnetism
PublikacjaIn 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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Square root RC Nyquist filter of fractional delay
PublikacjaIn 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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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublikacjaModern 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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Fractional Delay Filter Design for Sample Rate Conversion
PublikacjaRosnąca 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
PublikacjaW 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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Derivation of Schwinger variational principles.
PublikacjaZastosowano metodę Gerjuoy-Rau-Sprucha do skonstruowania zasad wariacyjnych Schwingera dla elementów macierzowych uogólnionego operatora przejścia.
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Functional differential equations
PublikacjaSformułowano 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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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn 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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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublikacjaIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell's equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Frequency response based identification of fractional order dynamical systems
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Modelling heat transfer in heterogeneous media using fractional calculus
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Modeling Heat Transfer in Heterogeneous Media Using Fractional Calculus
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Point to point control of fractional differential linear control systems
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A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS
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efficient fractional delay hilbert transform filter in the farrow structure
PublikacjaIn this paper the design and application of a Fractional Delay Hilbert Transform Filter (FDHTF) into an adaptive sub-sample delay estimation between two separated sinusoidal signals is considered. The FDHTF incorporates the functions of Hilbertian and variable fractional delay filtering of the incoming signal simultaneously, in one stage. In traditional approach each of these operations was performed separately. Obtained value...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Variable Fractional Delay Filter Design Using a Symmetric Window
PublikacjaIn this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family...
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A nearly optimal fractional delay filter design with asymmetric window
PublikacjaW pracy przedstawiono wyniki badań nad zastosowaniem asymetrycznego okna wyodrębnionego zawczasu z filtru optymalnego. Pokazano, że takie podejście przy zastosowaniu dodatkowej korekcji wzmocnienia filtru zależnej od opóźnienia filtru pozwala na projektowanie filtrów prawie optymalnych. W efekcie zaproponowana metoda łączy prostotę metody okien z jakością porównywalną do jakości filtrów optymalnych. Efektywność zaprezentowanej...
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Signal propagation in electromagnetic media described by fractional-order models
PublikacjaIn 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....