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Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer

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Abstract

The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials (FGM) (i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach. The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts - Khulais, University of Jeddah, Jeddah, Saudi Arabia

    Ibrahim A. Abbas

  2. Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Ibrahim A. Abbas

  3. Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

    Ibrahim A. Abbas

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  1. Ibrahim A. Abbas
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Correspondence to Ibrahim A. Abbas.

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Abbas, I.A. Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer. J. Cent. South Univ. 22, 1606–1613 (2015). https://doi.org/10.1007/s11771-015-2677-5

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  • DOI: https://doi.org/10.1007/s11771-015-2677-5

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