Fractional order generalized thermoelastic half-space subjected to ramp-type heating

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.