Yuriy Povstenko

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The different kinds of boundary conditions for standard and fractional diffusion and advection diffusion equations are analyzed. Near the interface between two phases there arises a transition region which state differs from the state of contacting media owing to the different material particle interaction conditions. Particular emphasis has been placed on(More)
The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion ) 0 ( R r   and a matrix ) (    r R being in perfect thermal contact at R r  is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 2 0   and , 2 0(More)
In this paper, the one-dimensional time-fractional diffusion–wave equation with the fractional derivative of orderα, 1 < α < 2, is revisited. This equation interpolates between the diffusion and the wave equations that behave quite differently regarding their response to a localized disturbance:whereas the diffusion equation describes a process,where a(More)
Two approaches resulting in two different generalizations of the space-time-fractional advection-diffusion equation are discussed. The Caputo time-fractional derivative and Riesz fractional Laplacian are used. The fundamental solutions to the corresponding Cauchy and source problems in the case of one spatial variable are studied using the Laplace transform(More)
The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The(More)
Different types of boundary conditions for the time-fractional heat conduction equation in a bounded domain are examined. A composed solid consisting of three domains is considered. Assuming that the thickness of the intermediate domain is small with respect to two other sizes and is constant, a three-dimensional heat conduction problem in the intermediate(More)
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