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Entropy 2015, 17(6), 4028-4039; doi:10.3390/e17064028

Generalized Boundary Conditions for the Time-Fractional Advection Diffusion Equation

Institute of Mathematics and Computer Science, Jan Długosz University in Częstochowa, Armii Krajowej 13/15, 42-200 Częstochowa, Poland
Academic Editors: J. A. Tenreiro Machado and António M. Lopes
Received: 4 May 2015 / Revised: 8 June 2015 / Accepted: 9 June 2015 / Published: 12 June 2015
(This article belongs to the Special Issue Complex and Fractional Dynamics)
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Abstract

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 the conditions of nonperfect diffusive contact for the time-fractional advection diffusion equation. When the reduced characteristics of the interfacial region are equal to zero, the conditions of perfect contact are obtained as a particular case. View Full-Text
Keywords: fractional calculus; non-Fickian diffusion; fractional advection diffusion equation; complex systems; nonperfect contact conditions fractional calculus; non-Fickian diffusion; fractional advection diffusion equation; complex systems; nonperfect contact conditions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Povstenko, Y. Generalized Boundary Conditions for the Time-Fractional Advection Diffusion Equation. Entropy 2015, 17, 4028-4039.

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