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  1. 2 Open Physics

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  1. 2 2013

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  1. 2 Povstenko Y.

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Fundamental solutions to time-fractional heat conduction equations in two joint half-lines

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Povstenko Y.
Open Physics
|
2013
|
vol. 11
|
issue 10
1284-1294
EN
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.
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Thermoelasticity of thin shells based on the time-fractional heat conduction equation

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Povstenko Y.
Open Physics
|
2013
|
vol. 11
|
issue 6
685-690
EN
The time-nonlocal generalizations of Fourier’s law are analyzed and the equations of the generalized thermoelasticity based on the time-fractional heat conduction equation with the Caputo fractional derivative of order 0 < α ≤ 2 are presented. The equations of thermoelasticity of thin shells are obtained under the assumption of linear dependence of temperature on the coordinate normal to the median surface of a shell. The conditions of Newton’s convective heat exchange between a shell and the environment have been assumed. In the particular case of classical heat conduction (α = 1) the obtained equations coincide with those known in the literature.
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