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F. Mainardi, “Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics,” In: A. Carpinteri and F. Mainardi, Eds., Fractals and Fractional Calculus in Continuum Mechanics, Springer, New York, 1997, pp. 291-348.

has been cited by the following article:

• TITLE: Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

  AUTHORS: Essam Bassiouny, Refaat Sabry

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.1 No.5, November 12, 2013

  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.