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1
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Archives of Mechanics
2014 Vol. 66, nr 3 147--172
EN Fractional continua is a generalisation of the classical continuum body. This new concept shows the application of fractional calculus in continuum mechanics. The advantage is that the obtained description is non-local. This natural non-locality is inherently a consequence of fractional derivative d[...]
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80%
Pomiary Automatyka Robotyka
2010 R. 14, nr 2 93-114
PL W pracy dokonano przeglądu wybranych zagadnień z zakresu rachunku niecałkowitego rzędu oraz teorii ciągłych układów liniowych stacjonarnych rzędu niecałkowitego, takich jak metody opisu, synteza regulatorów niecałkowitego rzędu, ich modelowanie oraz realizacja praktyczna, a także badanie stabilności[...]
EN The paper gives the review of the selected problems from calculus of non-integer order and theory of continuous-time linear systems of non-integer order such as description methods, synthesis of non-integer controllers, their modelling and practical realization and also stability checking of the con[...]
3
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper we study the properties of generalized fractional derivatives (GFDs) with respect to the reflection mapping in finite intervals. We introduce symmetric and antisymmetric derivatives in a given interval and a split of arbitrary function into [J]- projections - parts with well-defined re[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN A fractional differential equation of real order α, containing variable coefficient t β and a non-homogeneous term, is solved. The general solution is obtained as a sum of Meijer G-functions series determining the solution of a homogeneous counterpart of the considered equation and a series represen[...]
5
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN We study the properties of fractional differentiation with respect to reflection mapping in a finite interval. The symmetric and anti-symmetric fractional derivatives in a full interval are expressed as fractional differential operators in left or right subintervals obtained by subsequent partitions[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The Mellin transform method is applied to fractional differential equations with a right-sided derivative and variable potential. After solving the intermediate difference equation we arrive at the general solution of the problem in the form of a Meijer-G-function series. Using the symmetry properti[...]
7
80%
Przegląd Elektrotechniczny
2011 R. 87, nr 3 123-125
PL W niniejszym artykule przedstawiono uogólnienie metody różniczkowej i zbadano ją pod kątem przydatności w identyfikacji systemów zawierających elementy stopnia ułamkowego. Elementy te w równaniach różniczkowych wprowadzają pochodne ułamkowe, zaś w równaniach operatorowych pojawiają się w postaci ope[...]
EN This paper presents the parameters of identification method generalized for systems that for obtaining estimates of parameters of models use fractional differential equations i.e. systems containing elements of fractional degree. These elements introduce fractional derivatives to differential equat[...]
8
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Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
EN In this paper, we present an existence of monotonic solutions for a nonlinear multi term non-autonomous fractional differential equation in the Banach space of summable functions. The concept of measure of noncompactness and a fixed point theorem due to G. Emmanuelle is the main tool in carring out [...]
9
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Molecular and Quantum Acoustics
2003 Vol. 24 161-168
EN Applying Ter Haar, Alfrey, and Gross approximations, we have calculate distributions of viscoelastic relaxation times for relaxation functions given by Schiessel et al. Fractional derivatives calculus has been applied to Maxwell model of viscoelasticity and it has been proved by means of the Gross f[...]
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Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
2002 [Z] 42(2) 209-220
EN In this paper, Schauder fixed point theorem is used to prove an existence of positive continuous solutions for the nonlinear fractional order integral equation x(t) = h(t) + [lambda] I^a (f(x{t)) +g(x(t))), t € [0,1], a > 0 (E) , where f and g are nonlinear continuous functions and / is nondecreasin[...]
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Journal of Applied Computer Science Methods
2013 Vol. 5 No. 2 105--121
EN Electric energy stored insupercapacitors is associated with ion movement between the porous electrodes . This phenomenon can be described by dielectric relaxation model. Cole-Davidson relaxation model application reported in publications is difficult to use for control purposes. In the paper for imp[...]
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Computer Applications in Electrical Engineering
2015 Vol. 13 178--187
EN The paper describes method of parameters selection for control system with fractional order PIλDμ controller steering second order oscillated object. As a selection algorithm was used simulated annealing optimization method with random variant of cooling strategy. As a target f[...]
13
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Archives of Mechanics
2014 Vol. 66, nr 4 257--267
EN In this work, we apply the fractional order theory of thermoelasticity to a 1D problem of an infinitely long cylindrical cavity. Laplace transform techniques are used to solve the problem. Numerical results are computed and represented graphically for the temperature, displacement and stress distrib[...]
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Journal of Theoretical and Applied Mechanics
2016 Vol. 54 nr 1 295--304
EN In this work, we apply the fractional order theory of thermoelasticity to a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic medium in the form of a spherical shell subjected to sudden change in the temperature of its external boundary. Lapla[...]
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Journal of Theoretical and Applied Mechanics
2016 Vol. 54 nr 2 671--674
EN In this paper, for the first time, the geometrical interpretation of fractional strain tensor components is presented. In this sense, previous considerations by this author are shown in a new light. The fractional material and spatial line elements concept play a crucial role in the interpretation.
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Computational Methods in Science and Technology
EN In the note, recent efforts to derive fractional quantum mechanics are recalled. Some applications of a fractional approach to the Schrödinger equation are discussed as well.
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Fundamenta Informaticae
EN We investigate the unique solvability of a class of nonlinear nonlocal differential equations associated with degenerate linear operator at the fractional Caputo derivative. For the main results, we use the theory of fractional calculus and (L, p)-boundedness technique that based on the analysis of [...]
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Fundamenta Informaticae
EN In this paper, an approximate solution of the fractional type Rosenau-Hyman equation according to an appropriate initial condition will be obtained with the help of the reduced differential transform method (RDTM). The fractional derivatives are described in the Caputo sense. Comparing the methodolo[...]
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Fundamenta Informaticae
EN We present monotone convergence results for general iterative methods in order to approximate a solution of a nonlinear equation defined on a partially ordered linear topological space. The main novelty of the paper is that the operators appearing in the iterative method are not necessarily linear. [...]
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Technical Sciences / University of Warmia and Mazury in Olsztyn
2016 nr 19(3) 231--244
EN The time-fractional advection-diffusion equation with the Caputo time derivative is studied in a layer. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The logarithmicsingularity term is separated from the solution. Expressions amenable for numerica[...]
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