Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Yuriy Povstenko

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 611-622
  • ISSN: 2391-5455

Abstract

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The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.

How to cite

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Yuriy Povstenko. "Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition." Open Mathematics 12.4 (2014): 611-622. <http://eudml.org/doc/269178>.

@article{YuriyPovstenko2014,
abstract = {The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.},
author = {Yuriy Povstenko},
journal = {Open Mathematics},
keywords = {Fractional calculus; Diffusion-wave equation; Mittag-Leffler function; Robin boundary condition; Non-Fourier heat conduction; fractional heat conduction equation; fractional calculus; diffusion-wave equation; non-Fourier heat conduction},
language = {eng},
number = {4},
pages = {611-622},
title = {Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition},
url = {http://eudml.org/doc/269178},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Yuriy Povstenko
TI - Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 611
EP - 622
AB - The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.
LA - eng
KW - Fractional calculus; Diffusion-wave equation; Mittag-Leffler function; Robin boundary condition; Non-Fourier heat conduction; fractional heat conduction equation; fractional calculus; diffusion-wave equation; non-Fourier heat conduction
UR - http://eudml.org/doc/269178
ER -

References

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