Abstract
In this work, we will construct a mathematical model of an elastic material with constant parameters fills the half-space and the governing equations will be taken into the context of the fractional order generalized thermoelasticity theory ( Youssef, 2010). The medium is assumed initially quiescent and Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem of a medium subjected to ramp-type heating and traction free. The inverse of the Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effects of the fractional order parameter on all the studied felids.
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