 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| Mohamed I.A. Othman and Haitham M. Atef, "Conformable Fractional Order Theory in Thermoelasticity," Mech. Solids. 59 (2), 1180-1193 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
2 |
Pages |
1180-1193 |
| DOI |
10.1134/S0025654423602252 |
| Title |
Conformable Fractional Order Theory in Thermoelasticity |
| Author(s) |
Mohamed I.A. Othman (Faculty of Science, Department of Mathematics, Zagazig University, Zagazig, Egypt, m_i_a_othman@yahoo.com)
Haitham M. Atef (Faculty of Science, Department of Mathematics, Damanhur University, Damanhur, Egypt, hitham_ali@sci.dmu.edu.eg) |
| Abstract |
The fractional heat conduction equation in thermoelasticity by the definitions of Riemann-Liouville and Caputo has some shortcomings. In this paper, we introduce a conformable fractional order theory of thermoelasticity that remedies this shortcoming. Firstly, we derive the heat conduction equation based on the conformable fractional derivative. Then, the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. Finally, we apply these new governing equations to the problem of the general thermo material. The analytical expressions for physical quantities are obtained using normal mode analysis in the physical domain. These expressions are numerically calculated and graphically illustrated for a given material. The findings were predicted and tested in the presence and absence of fractional parameter. |
| Keywords |
Conformable fractional order theory, one relaxation time, thermo-elasticity, Riemann-Liouville and Caputo, normal mode analysis |
| Received |
03 November 2023 | Revised |
21 February 2024 | Accepted |
22 February 2024 |
| Link to Fulltext |
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