Essam Bassiouny^*, Refaat Sabry^*

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Department of Mathematics, Faculty of Science and Humanitarian Studies, Salman Bin AbdulAziz University, Al Kharj, KSA.
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Abstract: A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the boundary condition. The solution of the problem is first obtained in the Laplace transform domain. Furthermore, a complex inversion formula of the transform based on a Fourier expansion is used to get the numerical solutions of the field equations which are represented graphically.

Keywords: Fractional Order; Two Temperature; Generalized Thermoelectricity; Weak Diffusion; Thermal Loading; Piezoelectric Materials; Ceramics

Cite this paper: Bassiouny, E. and Sabry, R. (2013) Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials. Journal of Applied Mathematics and Physics, 1, 110-120. doi: 10.4236/jamp.2013.15017.

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