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Search results for: fractional derivatives and integrals
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublicationIn 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....
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublicationThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn 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...
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Fractional Differential Calculus
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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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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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublicationIn 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...
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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 neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublicationThis 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...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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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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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublicationZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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Evaluating the antibacterial activity of muramyl dipeptide derivatives, retro-tuftsin derivatives, and anthraquinone oligopeptides against a range of pathogenic bacteria
PublicationSearch for new and efficient antibiotic is crucial because of microbial drug resistance and problems with side effects of the administered medication. In this study, we evaluate the in vitro microbiological activity of muramyl dipeptide derivatives, retro-tuftsin derivatives (i.e., tuftsin with reversed amino acid sequences), and combinations of retro-tuftsin derivatives with substituted anthraquinones. The potency of the investigated...
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Catalytic Asymmetric Synthesis of Isochroman Derivatives
PublicationThe isochroman scaffold constitutes an important structural unit, which is present in various bioactive natural products and synthetic pharmaceutical compounds exhibiting wide arrays of biological properties. Hence the synthesis of this class of heterocyclic compounds in a stereoselective fashion is highly significant and desirable. In the last decade, a substantial advancement has been witnessed ln the catalytic asymmetric...
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The effect of anthraquinone derivatives on telomerase activity
Open Research DataThe data set contains images of the PCR products obtained from the Telomerase Repeated Amplification Protocol (TRAP). The effect of anthraquinone derivatives (TXT1-TXT9) on telomerase activity was comparatively examined using the following reference compounds: BIBR1532, TMPyP4 and mitoxantrone (MTX).
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublicationThis 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...
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Hedging with derivatives - Case of Polish market
PublicationThis paper attempts to show the ways of reaching the competitive advantage by hedging with derivatives in Poland. It shows the results of investigation of 50 Polish companies and comparison to the situation in high developed countries. Through broad review of relevant literature, the authors presented the correlation between hedging and competitive advantage. Moreover, paper shows the reasons, of differences between Poland and...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublicationThe 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...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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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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Studies on the influence of β-cyclodextrin derivatives on the physical stability of famotidine
PublicationThe usage of Fourier transform infrared spectroscopy, near infrared spectroscopy, differential scanning calorimetry and microscopy is presented in this work focused on the exploration of the effect of CD on the physical stability of famotidine (FAM). The most significant information was achieved by analysis of the second derivatives ofnear infrared (NIR) spectra recorded. Changes in the shape of spectra derivatives allow...
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Fractional Calculus and Applied Analysis
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Progress in Fractional Differentiation and Applications
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Fractal and Fractional
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Anticancer Properties of Amino Acid and Peptide Derivatives of Mycophenolic Acid
PublicationBackground: Although Mycophenolic Acid (MPA) is applied as prodrugs in clinic as an immunosuppressant, it also possesses anticancer activity. MPA acts as Inosine-5’-Monophosphate Dehydrogenase (IMPDH) inhibitor, where the carboxylic group at the end of the side chain interacts with Ser 276 of the enzyme via hydrogen bonds. Therefore, MPA derivatives with other polar groups indicated high inhibition too. On the other hand, potent...
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The effect of anthraquinone derivatives (C1-C9) on telomerase activity
Open Research DataThe data set contains images of the PCR products obtained from the Telomerase Repeated Amplification Protocol (TRAP). The effect of anthraquinone derivatives (C-C9) on telomerase activity was analyzed using lysates from drug-treatedcancer cell line.
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Synthesis and crystal structure of ferrocenyl benzothiazole derivatives
PublicationNovel ferrocenyl-containing benzothiazole derivatives were synthesised in moderate yields by one-pot α-amidoalkylation of ferrocene. The reaction conditions were critically evaluated and the crystal structure of one of the amidoalkylated ferrocenes was resolved. Oxidation of the obtained compounds led to known fully aromatic 2-ferrocenylbenzothiazole in 81 % yield, which represents a convenient alternative to earlier methods utilizing...
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublicationSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid (RA), a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, RA exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Indirect Measurement of Motor Current Derivatives in PMSM Sensorless Drives
PublicationMotor current derivatives contain useful information for control algorithms, especially in sensorless electric drives. The measurement of motor current derivatives in electric motors supplied by voltage source inverter can be performed using di/dt transducers. However, in such a solution additional sensors have to be installed, e.g. Rogowski coils. Another approach is to measure current derivatives indirectly – by oversampling...
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublicationSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid, a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, it exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Therapeutic Potential of Carnosine and Its Derivatives in the Treatment of Human Diseases
PublicationDespite significant progress in the pathogenesis, diagnosis, treatment, and prevention of cancer and neurodegenerative diseases, their occurrence and mortality are still high around theworld. The resistance of cancer cells to the drugs remains a significant problem in oncology today,while in the case of neuro-degenerative diseases, therapies reversing the process are still yet to be found. Furthermore, it is important to seek new...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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New Chalcones Derivatives With Potent Antitumor Activity And Their Metabolism In Vitro
PublicationChalcone derivatives exhibit a broad range of biological activities, with antioxidant and cytotoxic properties among the most studied. Despite numerous reports on chalcones as cytotoxic, and potentially anticancer agents, very little is know on their actual mechanism of activity. Generally, chalcones are considered as antimitotic agents, which interfere with tubulin assembly.We have recently developed a new class of chalcones with...
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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
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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Immunosuppressive properties of amino acid and peptide derivatives of mycophenolic acid
PublicationMycophenolic acid (MPA) was coupled with amino acids and biologically active peptides including derivatives of tuftsin to modify its immunosuppressive properties. Both amino acid unit in the case of simple MPA amides and modifications within peptide moiety of MPA - tuftsin conjugates influenced the observed activity. Antiproliferative potential of the obtained conjugates was investigated in vitro and MPA amides with threonine methyl...
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Acyl Meldrum's acid derivatives: application in organic synthesis
PublicationThis review is focused on one of the most important classes of Meldrum's acid derivatives commonly known as acyl Meldrum's acids. The preparation methods of these compounds are considered including the recently proposed and rather rarely used ones. The chemical properties of acyl Meldrum's acids are described in detail, including thermal stability and reactions with various nucleiophiles. The possible mechanisms of these transformations...
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Metal dusting phenomena of 501 AISI furnace tubes in refinery fractional distillation unit
PublicationThe purpose of this investigation was to conduct the failure analysis of 501 AISI furnace tubes places before distillation column in fractional distillation unit. The investigated furnace tubes were planned to work for ten years however after just two years of exploitation <30% of the material left. The observed corrosion process had the intense and complex character. The well-adhered shiny black deposits and deep, round pits were...
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Synthesis and antimicrobial activity of amino acid and peptide derivatives of mycophenolic acid
PublicationThe series of 16 novel amino acid and peptide mycophenolic acid (MPA) derivatives was obtained as potential antibacterial agents. Coupling of MPA with respective amines was optimized with condensing reagents such as EDCI/DMAP and T3P/TEA. Amino acid analogs were received both as methyl esters and also with the free carboxylic group. The biological activity of the products was tested on five references bacterial strains: Klebsiella...
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Improving the regulation of the derivatives market as an objective prerequisite for sustainable development of the global financial system
PublicationThe development of financial markets is characterized by the emergence of new financial instruments, in particular derivatives, the risk level analysis of which is complicated. Counterparties are not always fully aware of and do not adequately assess the potential risks of derivatives, which may lead to large financial losses and sometimes bankruptcies. The purpose of the study is to generalize approaches to regulating derivative...
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NADES propolis extracts - update 2023 and synthesis of derivatives of propolis ingredients
Open Research DataThis dataset contains results of our investigation aiming in determination of antimicrobial potential of the propolis extracts produced with deep eutectic solvents
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Cytotoxicity of anthraquinone derivatives (Compound 1-9) towards H226 cancer cell
Open Research DataThis study presents absorbance values of formazan product (converted from MTT) which corresponds to the cytotoxicity of anthraquinone derivatives (Compound 1-9) towards H226 cancer cells.
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Cytotoxicity of anthraquinone derivatives (Compound 1-9) towards A549 cancer cells
Open Research DataThis study presents absorbance values of formazan product (converted from MTT) which corresponds to the cytotoxicity of anthraquinone derivatives (Compound 1-9) towards A549 cancer cells.
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Cytotoxicity of anthraquinone derivatives (Compound 1-9) towards NHBE normal cells
Open Research DataThis study presents absorbance values of formazan product (converted from MTT) which corresponds to the cytotoxicity of anthraquinone derivatives (Compound 1-9) towards NHBE normal cells.