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 thermopiezoelasticity. 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.
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