wyświetlamy 1000 najlepszych wyników Pomoc
Wyniki wyszukiwania dla: FRACTIONAL DIFFERENTIAL EQUATION
-
JOURNAL OF DIFFERENTIAL EQUATIONS
Czasopisma -
FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
-
Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
-
KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublikacjaWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
-
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...
-
Thermal ablation modeling via the bioheat equation and its numerical treatment
PublikacjaThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
-
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...
-
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...
-
Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublikacjaIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
-
Methods of solving the Atkins equation determine shear angle with taking into consideration a modern fracture mechanics
PublikacjaIn the paper are presented methods of solving nonlinear Atkins equation . The Atkins equation describe shear angle with taking into account properties of material cutting. To solve Atkins equation has been used iterative methods: Newton method and simplified method of simple iteration. Method of simple iteration is presented in the form of Java application.
-
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...
-
Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublikacjaThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
-
Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
Publikacja -
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....
-
Considerations about the applicability of the Reynolds equation for analyzing high-speed near field levitation phenomena
Publikacjaequation for analyzing near field levitation (NFL) phenomena. Two separate approaches were developed, experimentally verified, and applied to meet the research objective. One was based on the Reynolds equation and the other was based on general conservation equations for fluid flow solved using computational fluid dynamic (CFD). Comparing the calculation results revealed that, for certain operating conditions, differences in the...
-
On neutral differential equations and the monotone iterative method
PublikacjaThe application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving sufficient conditions which guarantee that such problems have solutions. This approach is new and to the Authors' knowledge, this is the first paper when the monotone iterative method is applied to neutral first-order differential equations with deviating...
-
A Criterion for Conditional Instability by the First Approximation for Solutions of Differential Systems
Publikacja -
Method of lines for Hamilton-Jacobi functional differential equations.
PublikacjaInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
-
Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublikacjaThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
-
Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
PublikacjaThe sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting...
-
On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublikacjaIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
-
Differential analysis of dynamic immittance spectra
PublikacjaThis work presents a new approach to the analysis of immittance spectrograms of systems characterised by non-stationarity. The possibility of linking the evolution of the immittance response with changes in the parameters describing the system is achieved by introducing a spectrum in differential form. By using the above procedure, it becomes possible to separate elements with a dependence (or lack thereof) from an independent...
-
Analysis of Positioning Error and Its Impact on High Frequency Performance Parameters of Differential Signal Coupler of Differential Signal Coupler
PublikacjaThis paper presents the analysis of the effect of differential signal coupler positioning accuracy on its high frequency performance parameters for contact-less high speed chip-to-chip data transmission on PCB application. Our considerations are continuation of the previous works on differential signal coupler concept, design methodology and analysis for high speed data transmission monitoring presented in [1, 2]. The theoretical...
-
A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublikacjaThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
-
Equation of state for Eu-doped SrSi2O2N2
Publikacja -
Approximated boundary conditions of the equation of difussion
PublikacjaProblem podejmowany w pracy dotyczy warunku brzegowego w równaniach fizyki matematycznej, opisujących procesy migracji zanieczyszczeń. W szczególności skoncentrowano się na badaniu wpływu na rozwiązanie przyjmowanych w rozwiązaniach numerycznych aproksymacji ''odpływowego'' warunku brzegowego w jednowymiarowym równaniu adwekcji - dyspersji. Rozważania teoretyczne przeprowadzono w oparciu o rozwiązania analityczne oraz numeryczne...
-
The application of Monod equation to denitrification kinetics description in the moving bed biofilm reactor (MBBR)
PublikacjaIn this paper, the kinetic constants Vmax and KCOD occurring in the Monod equation, which describe the denitrification process in the moving bed, are determined. For this purpose, a laboratory moving bed biofilm reactor (MBBR) was used. The filling of the reactor consisted of EvU Perl carriers. The experiment was carried out with an excess of nitrate, and denitrification rate was dependent on the concentration of external organic...
-
Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition
PublikacjaResearch on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However,...
-
Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublikacjaThis paper presents the synthesis of an adaptive PID type controller in which the variable-order fractional operators are used. Due to the implementation difficulties of fractional order operators, both with a fixed and variable order, on digital control platforms caused by the requirement of infinite memory resources, the fractional operators that are part of the discussed controller were approximated by recurrent neural networks...
-
Method of lines for nonlinear first order partial functional differential equations.
PublikacjaClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
-
DIFFERENTIAL EQUATIONS
Czasopisma -
Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublikacjaVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
-
Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
-
Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublikacjaWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
-
Systems of boundary value problems of advanced differential equations
PublikacjaThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
-
Compensation of magnetic disturbances caused by sensors in a differential magnetometric system
PublikacjaStudy of low magnetic fields necessitates the use of precision magnetometers working in a differential system. Minimization of this error is a substantial issue in the case of magnetometers working in a differential system on a mobile platform. The compensation method of heading error consists in taking measurements of changes in magnetic induction with the use of the tested magnetometer for various locations of the sensor in relation...
-
Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublikacjaThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
-
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.
-
Fractional Calculus and Applied Analysis
Czasopisma -
Progress in Fractional Differentiation and Applications
Czasopisma -
Fractal and Fractional
Czasopisma -
Simulating propagation of coherent light in random media using the Fredholm type integral equation
PublikacjaStudying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g....
-
Quantum corections to SG equation solutions and applications
Publikacja -
Aerated grit chambers hydraulic design equation.
PublikacjaW pracy zaproponowano metodę wymiarowania piaskowników napowietrzanych. Jej głównymi elementami są wyznaczanie niezbędnej intensywności aeracji ścieków, pola ich prędkości oraz trajektorii cząstek zawiesiny.
-
Low energy differential elastic electron scattering from acetonitrile (CH3CN)
PublikacjaMeasurements of elastic differential cross sections for electron scattering from acetonitrile (CH3CN) have been performed utilizing a crossed electron-molecular beam experiment and with the relative flow method, for the incident electron energy range of 0.7 eV–30 eV and the scattering angle range of 10◦–130◦. These differential cross sections have been used to calculate the elastic integral and momentum- transfer cross sections,...
-
Implicit difference methods for first order partial differential functional equations
PublikacjaKlasyczne rozwiązania problemów początkowo brzegowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
-
Modelling of joining route segments of differential curvature
PublikacjaThe paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph...
-
The interpretation of the parameters of the equation used for the extrapolation of apparent molar volumes of the non-electrolyte (solutes) to the infinite dilution
PublikacjaThe paper discusses how to interpret the parameters of the basic equation used for the extrapolation of the apparent molar volume of the solute to infinite dilution. The common misunderstandings and oversimplifications have been pointed out. We present the alternative ways of the data interpretation that can be used to eliminate these obvious but frequent mistakes.
-
Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublikacjaIn this paper, we retrieve some traveling wave, periodic solutions, bell shaped, rational, kink and anti-kink type and Jacobi elliptic functions of Burger’s equation and Shallow water wave equation with the aid of various integration schemes like improved -expansion scheme and Jacobi elliptic function method respectively. We also present our solutions graphically in various dimensions.
-
Application of the numerical-analytic method for systems of differential equations with parameter
PublikacjaThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument