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- Yuriy Povstenko
- Computers & Mathematics with Applications
- 2012

- Yuriy Povstenko
- Applied Mathematics and Computation
- 2015

- Yuriy Povstenko
- Entropy
- 2015

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)

- Yuriy Povstenko
- Entropy
- 2013

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)

- Yuri Luchko, Francesco Mainardi, Yuriy Povstenko
- Computers & Mathematics with Applications
- 2013

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)

- Y. Z. Povstenko
- 2011

Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the Hankel transform with respect to the radial coordinate r, the finite Fourier transform with respect to the angular coordinate… (More)

- Yuriy Povstenko, Tamara Kyrylych
- Entropy
- 2017

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)

- Yuriy Povstenko
- Computers & Mathematics with Applications
- 2012

- Yuriy Povstenko, Tamara Kyrylych, Grazyna Rygal
- Entropy
- 2017

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)

- Yuriy Povstenko
- ICFDA'14 International Conference on Fractional…
- 2014

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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