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Search results for: finite-difference discretization
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Ireneusz Kreja dr hab. inż.
PeopleGraduated from the mathematical class at the Nicolaus Copernicus High School in Gdańsk (1974). Master of Sciences in Civil Engineering after studies at Gdansk University of Technology (GUT), Poland (1974-1979). Since 1979 became an employee of the GUT. In 1989 earned a Ph.D. degree in Civil Engineering (with grade "Summa cum Laude") from the GUT. In 2008 obtained a D. Sc. (Habilitation) degree in Civil Engineering (with grade...
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Determination of time delay between ventricles contraction using impedance measurements
PublicationThe paper presents a novel approach to assessment of ventricular dyssynchrony basing on multichannel electrical impedance measurements. Using a proper placement of electrodes, the sensitivity approach allows estimating time difference between chambers contraction from over determined nonlinear system of equations. The theoretical considerations which include Finite Element Method simulations were verified using measurements on...
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Coherent-wave Monte Carlo method for simulating light propagation in tissue
PublicationSimulating propagation and scattering of coherent light in turbid media, such as biological tissues, is a complex problem. Numerical methods for solving Helmholtz or wave equation (e.g. finite-difference or finite-element methods) require large amount of computer memory and long computation time. This makes them impractical for simulating laser beam propagation into deep layers of tissue. Other group of methods, based on radiative...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublicationIn 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...
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How to render FDTD computations more effective using agraphics accelerator.
PublicationGraphics processing units (GPUs) for years have been dedicated mostly to real time rendering. Recently leading GPU manufactures have extended their research area and decided to support also graphics computing. In this paper, we describe an impact of new GPU features on development process of an efficient finite difference time domain (FDTD) implementation.
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GPR simulations for diagnostics of a reinforced concrete beam
PublicationThe most popular technique for modelling of an electromagnetic field, the finite difference time domain (FDTD) method, has recently become a popular technique as an interpretation tool for ground penetrating radar (GPR) measurements. The aim of this study is to detect the size and the position of damage in a reinforced concrete beam using GPR maps. Numerical simulations were carried out using the finite differ-ence time domain...
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Using GPUs for Parallel Stencil Computations in Relativistic Hydrodynamic Simulation
PublicationThis paper explores the possibilities of using a GPU for complex 3D finite difference computation. We propose a new approach to this topic using surface memory and compare it with 3D stencil computations carried out via shared memory, which is currently considered to be the best approach. The case study was performed for the extensive computation of collisions between heavy nuclei in terms of relativistic hydrodynamics.
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The modelling method of discrete-continuous systems
PublicationThe paper introduces a method of discrete-continuous systems modelling. In the proposed method a three-dimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit...
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Hybrid technique for the analysis of circular waveguide junctions loaded with ferrite posts
PublicationThis study presents a hybrid technique for the analysis of circular waveguide junctions loaded with axially symmetrical ferrite posts of irregular shape. The method is based on a combination of the finite-difference frequency- domain technique with a mode-matching technique. The proposed approach is validated by comparing the presented results with numerical ones obtained from commercial software. The application of a cylindrical...
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OpenGL accelerated method of the material matrix generation for FDTD simulations
PublicationThis paper presents the accelerated technique of the material matrix generation from CAD models utilized by the finite-difference time-domain (FDTD) simulators. To achieve high performance of these computations, the parallel-processing power of a graphics processing unit was employed with the use of the OpenGL library. The method was integrated with the developed FDTD solver, providing approximately five-fold speedup of the material...
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A high-accuracy complex-phase method of simulating X-ray propagation through a multi-lens system
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens...
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Recurrence scheme for FDTD-compatible discrete Green's function derived based on properties of Gauss hypergeometric function
PublicationIn this paper, the formulation of one-dimensional FDTD (Finite-difference time-domain)-compatible discrete Green's function (DGF) is derived based on the Gauss hypergeometric function (GHF). The properties of GHF make it possible to derive the recurrence scheme only in the time domain for the DGF generation. Furthermore, this recurrence scheme is valid for any stable time-step size and can be implemented using standard numerical...
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Towards an efficient multi-stage Riemann solver for nuclear physics simulations
PublicationRelativistic numerical hydrodynamics is an important tool in high energy nuclear science. However, such simulations are extremely demanding in terms of computing power. This paper focuses on improving the speed of solving the Riemann problem with the MUSTA-FORCE algorithm by employing the CUDA parallel programming model. We also propose a new approach to 3D finite difference algorithms, which employ a GPU that uses surface memory....
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Resonance Frequency Calculation of Spherical Microstrip Structure Using Hybrid Technique
PublicationIn this paper the spherical microstrip structure is considered. The structure is composed of a metallic patch with an arbitrary shape placed on a dielectric coated metallic sphere. In the analysis the hybrid technique is utilized. In this approach the finite-difference technique is applied in a cavity model to determine the current basis functions on the patch. Next, using method of moments, the resonance frequency of the structure...
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Numerical analysis of elastic wave propagation in unbounded structures
PublicationThe main objective of this paper is to show the effectiveness and usefulness of the concept of an absorbing layer with increasing damping (ALID) in numerical investigations of elastic wave propagation in unbounded engineering structures. This has been achieved by the authors by a careful investigation of three different types of structures characterised by gradually increasing geometrical and mathematical description complexities....
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Numerical FDM modelling of wave propagation in concrete structure
PublicationThe article presents application of finite difference method to damage detection and its size evaluation in concrete structure by elastic wave propagation method. The simulations of wave propagation in concrete structure were performed for six different damage scenarios. Damages were modelled as areas with changed material properties. Investigation focused on the influence of damage size on the energy of wave reflection. Presented...
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Zdzisław Kowalczuk prof. dr hab. inż.
PeopleZdzislaw Kowalczuk received his M.Sc. degree in 1978 and Ph.D. degree in 1986, both in Automatic Control from Technical University of Gdańsk (TUG), Gdańsk, Poland. In 1993 he received his D.Sc. degree (Dr Habilitus) in Automatic Control from Silesian Technical University, Gliwice, Poland, and the title of Professor from the President of Poland in 2003. Since 1978 he has been with Faculty of Electronics, Telecommunications and Informatics...
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Wykorzystaniem metody elementów skończonych w obliczaniu stateczności silosu z blachy falistej = Finite element method in determining stability of with corrugated walls strengthened by vertical columns of thin walled open cross section
PublicationGwałtowny rozwój zastosowania MES w działalności inżynierskiej nastąpił w połowie lat osiemdziesiątych w związku z pojawieniem się komputerów osobistych (PC), na które przeniesione zostały programy z dużych jednostek obliczeniowych. W ten sposób efektywne narzędzie rozwiązywania problemów analiz i projektowania jakim jest MES, stało się powszechnie dostępne. W artykule przedstawiono zastosowanie MES w analizie stateczności stalowego...
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A New Expression for the 3-D Dyadic FDTD-Compatible Green's Function Based on Multidimensional Z-Transform
PublicationIn this letter, a new analytic expression for the time-domain discrete Green's function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublicationWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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SIMPLIFIED DYNAMIC MODEL OF ROTATING BEAM
PublicationIn the paper a hybrid model of rotating beam is presented. It was obtained by using two methods: modal decomposition and spatial discretization. Reduced modal model was built for the system without the load related to inertia forces that occur during beam rotation. This inertia load was next modeled by using the method of simply spatial discretization and combined with reduced modal model. This approach allows to obtain accurate...
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Numerical simulation of hardening of concrete plate
PublicationThe paper presents a theoretical formulation of concrete curing in order to predict temperature evolution and strength development. The model of heat flow is based on a well-known Fourier equation. The numerical solution is implemented by means of the Finite Difference Method. In order to verify the model, the in situ temperature measurements at the top plate of a road bridge were carried out. A high agreement between numerical...
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Exact modal absorbing boundary condition for waveguide simulations - discrete Green's function approach
PublicationA modal absorbing boundary condition (ABC) based on the discrete Green's function (DGF) is introduced and applied for termination of waveguides simulated by means of the finite-difference time-domain (FDTD) method. The differences between the developed approach and implementations already demonstrated in the literature are presented. By applying DGF, a consistent theoretical approach to modal ABC in the FDTD method is obtained....
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublicationThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow
PublicationTwo explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free...
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Numerical modeling of GPR field in damage detection of a reinforced concrete footbridge
PublicationThe paper presents a study on the use of the ground penetrating radar (GPR) method in diagnostics of a footbridge. It contains experimental investigations and numerical analyses of the electromagnetic field propagation using the finite difference time domain method (FDTD). The object of research was a reinforced concrete footbridge over a railway line. The calculations of the GPR field propagation were performed on a selected cross-section...
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Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublicationInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
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Mixed, quantum-classical description of electron density transfer in the collision process
PublicationIn this work, we investigate an ion-atom model describing the time-dependent evolution of electron density during the collision. For a S3+- H system, numerical simulations are based on classical trajectory calculations, and the electron density behaviour is described with the time-dependent Schrödinger equation. We apply the finite difference method to obtain quantitative insights into the charge transfer dynamics, providing detailed...
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On the crack front curvature in bonded joints
PublicationStandard tests of adhesively bonded specimens are likely to produce heterogeneous stress distribution along the crack front and its vicinity. High separation rate mode I dominated fracture test is performed.Observation of post mortem fractured surfaces with an optical microscope reveals characteristic features of mixed mode I/III fracture near the sides of the specimen but not in the middle. At first, finite elements calculations...
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Simulating coherent light propagation in a random scattering materials using the perturbation expansion
PublicationMultiple scattering of a coherent light plays important role in the optical metrology. Probably the most important phenomenon caused by multiple scattering are the speckle patterns present in every optical imaging method based on coherent or partially coherent light illumination. In many cases the speckle patterns are considered as an undesired noise. However, they were found useful in various subsurface imaging methods such as...
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Fast implementation of FDTD-compatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finite-difference time domain (FDTD)-compatible Green's function on a multicore processor is presented. Recently, closed-form expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations...
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Interaction of PDA monomers with Au
Open Research DataThis dataset contains supplementary information in the form of Electrostatic difference potential (EDP) map, density of states (DOS) spectra, and adsorption geometries of polydopamine PDA monomers on the Au surface. PDA was modelled either as the oxidised (indolequinone, IQ) and reduced (dihydroxyindole, DHI) chemistries.
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Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow
PublicationThe paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. Thi smakes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a...
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Acceleration of the DGF-FDTD method on GPU using the CUDA technology
PublicationWe present a parallel implementation of the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method on a graphics processing unit (GPU). The compute unified device architecture (CUDA) parallel computing platform is applied in the developed implementation. For the sake of example, arrays of Yagi-Uda antennas were simulated with the use of DGF-FDTD on GPU. The efficiency of parallel computations...
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Alternative cogeneration thermodynamic cycles for domestic ORC
PublicationThe Organic Flash Cycle (OFC) is suggested as a vapor power cycle that could potentially improve the efficiency of utilization of the heat source. Low and medium temperature finite thermal sources are considered in the cycle. Additionally the OFC’s aim is to reduce temperature difference during heat addition. The study examines 2 different fluids. Comparisons are drawn between the OFC and an optimized basic Organic Rankine Cycle...
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Parallel implementation of the DGF-FDTD method on GPU Using the CUDA technology
PublicationThe discrete Green's function (DGF) formulation of the finite-difference time-domain method (FDTD) is accelerated on a graphics processing unit (GPU) by means of the Compute Unified Device Architecture (CUDA) technology. In the developed implementation of the DGF-FDTD method, a new analytic expression for dyadic DGF derived based on scalar DGF is employed in computations. The DGF-FDTD method on GPU returns solutions that are compatible...
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A high-accuracy method of computation of x-ray waves propagation through an optical system consisting of many lenses
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated...
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublicationThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Diagnostics of pillars in St. Mary’s Church (Gdańsk, Poland) using the GPR method
PublicationThe main goal of this study was non-destructive evaluation of pillars in the St. Mary’s Church (Gdańsk, Poland) using the ground penetrating radar (GPR) technique. The GPR inspection was conducted on four brick masonry pillars and five pillars strengthened by reinforced concrete jacketing. Data were acquired with a 2 GHz antenna along longitudinal and transverse profiles. The study involved the estimation of the electromagnetic...
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Analytical Expression for the Time-Domain Discrete Green's Function of a Plane Wave Propagating in the 2-D FDTD Grid
PublicationIn this letter, a new closed-form expression for the time-domain discrete Green's function (DGF) of a plane wave propagating in the 2-D finite-difference time-domain (FDTD) grid is derived. For the sake of its verification, the time-domain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2-D total-field/scattered-field (TFSF) FDTD simulations. Such an implementation of...
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Global sensitivity analysis of membrane model of abdominal wall with surgical mesh
PublicationThe paper addresses the issue of ventral hernia repair. Finite Element simulations can be helpful in the optimization of hernia parameters. A membrane abdominal wall model is proposed in two variants: a healthy one and including hernia defect repaired by implant. The models include many uncertainties, e.g. due to variability of abdominal wall, intraabdominal pressure value etc. Measuring mechanical properties with high accuracy...
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Hybridization of the FDTD method with use of the discrete Green's function
PublicationIn this contribution, a hybrid technique is presented which combines the finite-difference time-domain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many free-space cells. Therefore, the hybrid method was developed which is applicable to complex...
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Analytical Expression for the Time-Domain Green's Function of a Discrete Plane Wave Propagating in the 3-D FDTD Grid
PublicationIn this paper, a closed-form expression for the time-domain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3-D finite-difference time-domain (FDTD) grid is derived. In order to verify our findings, the time-domain implementation of the DPW-injection technique is developed with the use of the derived expression for 3-D total-field/scattered-field (TFSF) FDTD simulations. This implementation requires computations...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Implementation of FDTD-Compatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finite-difference time domain (FDTD)-compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closed-form expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision...
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A novel heterogeneous model of concrete for numerical modelling of ground penetrating radar
PublicationThe ground penetrating radar (GPR) method has increasingly been applied in the non-destructive testing of reinforced concrete structures. The most common approach to the modelling of radar waves is to consider concrete as a homogeneous material. This paper proposes a novel, heterogeneous, numerical model of concrete for exhaustive interpretation of GPR data. An algorithm for determining the substitute values of the material constants...
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Double-diffusive natural convection energy transfer in magnetically influenced Casson fluid flow in trapezoidal enclosure with fillets
PublicationThe prime motive of this disquisition is to deal with mathematical analysis of natural convection energy transport driven by combined buoyancy effects of thermal and solutal diffusion in a trapezoidal enclosure. Casson fluid rheological constitutive model depicting attributes of viscoelastic liquids is envisioned. The influence of the inclined magnetic field governed by Lorentz field law is also considered. To raise the essence...
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Database of the thermal ablation model
Open Research DataThermal ablation is a low invasive technique which eliminates cancerous tissue using high temperature. The presented database was used to show the temperature distribution for t=600[s] in two cases: when the value of the thermal conductivity of tissue k(x;T) is constant and for the variable k(x;T). In addition, using these data we showed the difference...
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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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Point to point control of fractional differential linear control systems
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