Comptes Rendus
Fractional calculus in one-dimensional isotropic thermo-viscoelasticity
Comptes Rendus. Mécanique, Volume 341 (2013) no. 7, pp. 553-566.

A new fractional relaxation operator is derived using the methodology of fractional calculus. The governing coupled fractional differential equations in the frame of the thermo-viscoelasticity with fractional order heat transfer are applied to the one-dimensional problem with heat sources. Laplace transform and state space techniques are used to get the solution. According to the numerical results and its graphs, conclusion about the new theory of thermo-viscoelasticity has been constructed. The theories of coupled thermo-viscoelasticity and of generalized thermo-viscoelasticity with one relaxation time follow as limit cases.

Published online:
DOI: 10.1016/j.crme.2013.04.001
Keywords: Thermo-viscoelasticity, Fractional relaxation function, Non-Fourier heat conduction, State space approach, Laplace transforms, Fractional calculus

Magdy A. Ezzat 1; Ahmed S. El-Karamany 2; Alaa A. El-Bary 3; Mohsen A. Fayik 1

1 Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
2 Department of Mathematical and Physical Sciences, Nizwa University, Nizwa 611, P.O. Box 1357, Oman
3 Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt
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     title = {Fractional calculus in one-dimensional isotropic thermo-viscoelasticity},
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     pages = {553--566},
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Magdy A. Ezzat; Ahmed S. El-Karamany; Alaa A. El-Bary; Mohsen A. Fayik. Fractional calculus in one-dimensional isotropic thermo-viscoelasticity. Comptes Rendus. Mécanique, Volume 341 (2013) no. 7, pp. 553-566. doi : 10.1016/j.crme.2013.04.001.

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