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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.doi:10.4236/jamp.2013.15017 fatcat:b4jckgoliba27d7rkqsqseb5ye