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Zeszyty Naukowe / Akademia Morska w Szczecinie
2012 nr 29 (101) 109-116
PL W artykule przedstawiono możliwość modelowania przetworników pomiarowych stosowanych w obiektach transportowych przy zastosowaniu rachunku różniczkowo-całkowego rzędów niecałkowitych (ang. fractional calculus). W pracy dokonano analizy właściwości dynamicznych w ujęciu czasowym i częstotliwościowym [...]
EN The paper presents the possibility of modelling transducers used in transport facilities using fractional calculus and analyses of the dynamic properties in terms of time and frequency for the measuring transducer with a seismic mass. Pointed out the benefits of fractional calculus in the descriptio[...]
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Prace Naukowe Politechniki Szczecińskiej. Instytut Informatyki
1998 Nr 537(1) 7-326
PL Teoria logicznego rachunku różniczkowego jest jednym z kierunków algebry logiki i zorientowania na rozwiązywanie problemów projektowania logicznego. Osiągnięcia przemysłu w zakresie elementów wielowartościowych stymulują badania nad rozwinięciem LRR. W niniejszej pracy, po raz pierwszy, metody LRR r[...]
EN Logic Differential (LD) Calculus theory is one of the directions of algebra of logic. It is oriented toward solving the Logic Design problems. The achievements of industry on Multiple-Valued Logic (MVL) gates has stimulated research on generalization of LD Calculus. In the thesis, for the first ti[...]
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Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
2014 Vol. 47, nr 2 459--464
EN A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds, which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus. A derivation of the enveloping algebra can be r[...]
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Autobusy : technika, eksploatacja, systemy transportowe
2017 R. 18, nr 12 1050--1055, CD
PL W artykule przedstawiono zastosowanie rachunku różniczkowego niecałkowitych rzędów (ang. fractional calculus) do opisu dynamiki zjawisk układów pneumatycznych. W budowie modeli matematycznych, analizowanych układów dynamicznych, wykorzystano definicję Riemanna-Liouville’a pochodno-całki niecałkowite[...]
EN Rapid development of technology which occurred at the turn of the 19th and 20th century has enforced development of new models describing reality, especially the technical objects working in extreme conditions or characterized by extreme parameters (a super-capacitor, a transmission line of infinite[...]
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Autobusy : technika, eksploatacja, systemy transportowe
2017 R. 18, nr 12 1056--1060, CD
PL W artykule przedstawiono wyniki badań laboratoryjnych układu wtryskowego, silnika spalinowego, pod kątem weryfikacji badań symulacyjnych wybranych układów pneumatycznych opisanych rachunkiem różniczkowo-całkowym niecałkowitych rzędów (ang. fractional calculus), przeprowadzonych w Części 1 artykułów.[...]
EN The Part 2 of these papers, deals with laboratory tests of a pneumatic transducer. Measurements have been taken and a real pneumatic system is analyzed and compared with a mathematical model. The analysis uses fractional calculus and is carried out with respect to time and frequency.
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TTS Technika Transportu Szynowego
2015 R. 22, nr 12 1331--1334, CD
PL W artykule przedstawiono zastosowanie rachunku różniczkowego do wyznaczania postaci równań różniczkowych rodziny krzywych. Postać równań różniczkowych otrzymano w wyniku eliminacji parametrów z równań opisujących rodzinę poszczególnych krzywych. Eliminacja parametrów została wykonana w wyniku kilkuk[...]
EN The article describes the use of differential calculus to determine the form of differential equations family of curves. Form of differential equations obtained by eliminating the parameters of the equations describing the different family of curves. Elimination of the parameters has been performed [...]
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Autobusy : technika, eksploatacja, systemy transportowe
2017 R. 18, nr 12 786--791, CD
PL W artykule przeanalizowano pochodną Grünwalda-Letnikova ƒ(ƞ)(t) w odniesieniu do klasycznego zagadnienia prędkości, jako pierwszej pochodnej funkcji drogi w czasie ƒ(1)(t). Autor argumentuje, że dodatnia pochodna Grünwalda-Letnikova nie spełnia twierdzenia Lagrange’a, co wiąże [...]
EN The paper analyses Grünwald-Letnikov ƒ(ƞ)(t) derivative in space of first order derivative ƒ(1)(t) and also analyses the classical interpretation of derivative of path function as velocity. The author argues that the Grünwald-Letnikov positive derivative does not fulfil the Lag[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 455--465
EN This paper presents models of economic growth for all states of the European Union (EU), since either 1970 or the year of accession to the EU. Both integer and fractional order models are obtained, where the gross domestic product (GDP) is a function of the country’s land area, gross capital formati[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 449--454
EN The problem of stability of the Gr¨unwald-Letnikov-type linear fractional-order discrete-time systems with delays is discussed. For the stability analysis of the considered systems the Z -transform is used. The sufficient conditions for the asymptotic stability of the considered systems are presente[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 427--432
EN In this paper, a novel anti-windup strategy is presented. It is based on using fractional variable order integrator instead of integer order one in PID controller. It is shown that among four different types of variable order derivative definitions, only one gives satisfactory results – comparable, [...]
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Reports on Geodesy
2004 nr 3/70 67-74
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2017 Vol. 65, nr 4 449--457
EN At the beginning of the paper, the fractional calculus is briefly presented. Then, the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model, a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected [...]
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Archives of Transport System Telematics
EN The section of the paper on simulation studies presents the application of fractional calculus to describe the dynamics of pneumatic systems used in telematics. In the construction of mathematical models of the analyzed dynamic systems, the Riemann-Liouville definition of non-integer order was used.[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 475--484
EN The paper concerns an analysis for SubIval (the subinterval-based method for fractional derivative computations in initial value problems). A time step size adaptive solver is discussed, for which the formula of a local truncation error is derived. A general form for a system of linear equations is [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 485--493
EN The applicability of fractional calculus in system engineering outperforms classic identification techniques due to its ability to depict physical phenomena with increased accuracy. The present study explores the increased accuracy and flexibility of a fractional order model applied to an experiment[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 5 737--745
EN Continuum models generalized by fractional calculus are used in different mechanical problems. In this paper, by using the conformable fractional derivative (CFD) definition, a general form of Eringen non-local theory as a fractional non-local model (FNM) is formulated. It is then used to study the [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
EN The optimal design of excitation signal is a procedure of generating an informative input signal to extract the model parameters with maximum pertinence during the identification process. The fractional calculus provides many new possibilities for system modeling based on the definition of a derivat[...]
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Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
2014 Vol. 19 29--36
EN In the paper the authors analyse different shapes of an hourglass for the linearity of their graduation. We also assume that any hourglass (more precisely, each of the two congruent parts) has the shape of a solid of revolution and any cross section at height h of this hourglass depends on the base [...]
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Journal of Applied Analysis
EN Using the concept of the normal cone to a multifunction we define a derivative for a complex-valued multifunction of one complex variable being a natural generalization of the ordinary complex derivative for holomorphic functions. Using results obtined by Mordukhovich, we develop a full calculus and[...]
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Problemy Nauk Stosowanych
2014 T. 2 69--82
PL Wstęp i cele: W pracy przedstawiono dwa zagadnienia mechaniczne, a mianowicie analizę prędkości korbowodu oraz badanie prędkości wznoszenia się mechanizmu przegubowego. Głównym celem pracy jest opracowanie modelu analitycznego oraz numerycznego dla analizy prędkości korbowodu i przegubu. Materiał i [...]
EN Introduction and aims: The paper presents two mechanical problems, namely the analysis of the velocity of the connecting-rod and the test velocity of bar link-age mechanism. The main aim of this work is to develop the analytical and numerical model for the analysis of the velocity of the connecting-[...]
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