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Povstenko Y.,Jan Dlugosz University in Czestochowa
Central European Journal of Physics | Year: 2013

Heat conduction in two joint half-lines is considered under the condition of perfect contact, i.e. when the temperatures at the contact point and the heat fluxes through the contact point are the same for both regions. The heat conduction in one half-line is described by the equation with the Caputo time-fractional derivative of order α, whereas heat conduction in another half-line is described by the equation with the time derivative of order β. The fundamental solutions to the first and second Cauchy problems as well as to the source problem are obtained using the Laplace transform with respect to time and the cos-Fourier transform with respect to the spatial coordinate. The fundamental solutions are expressed in terms of the Mittag-Leffler function and the Mainardi function. © 2013 Versita Warsaw and Springer-Verlag Wien. Source


Girek T.,Jan Dlugosz University in Czestochowa
Journal of Inclusion Phenomena and Macrocyclic Chemistry | Year: 2013

In the paper cyclodextrin-based (CD) polyrotaxanes are presented in the aspect of their syntheses and properties allowing various applications. The text consists of four parts, which describe CD-based polyrotaxanes with threads containing poly(ethylene oxide), poly (4,4′-diphenylenevinylene), polyfluorene and other chains. Conclusion shows new trends connected with this theme. © 2012 Springer Science+Business Media Dordrecht. Source


The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically. © 2011 Springer Science+Business Media B.V. Source


Povstenko Y.,Jan Dlugosz University in Czestochowa
Nonlinear Dynamics | Year: 2010

The paper is concerned with analysis of time-fractional diffusion-wave equation with Caputo fractional derivative in a half-space. Several examples of problems with Dirichlet and Neumann conditions at the boundary of a half-space are solved using integral transforms technique. For the first and second time-derivative terms, the obtained solutions reduce to the solutions of the ordinary diffusion and wave equations. Numerical results are presented graphically for various values of order of fractional derivative. © 2009 Springer Science+Business Media B.V. Source


Povstenko Y.Z.,Jan Dlugosz University in Czestochowa
Journal of Thermal Stresses | Year: 2013

The problem of fractional heat conduction in a composite medium consisting of two semi-infinite regions being in perfect thermal contact is considered. The heat conduction in each region is described by the time-fractional heat conduction equations with the Caputo derivative of fractional order α and β, respectively. The solution is obtained using the Laplace transform with respect to time and is expressed in terms of the Mittag-Leffler function and Mainardi function. Numerical results are illustrated graphically. © 2013 Copyright Taylor and Francis Group, LLC. Source

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