Abstract
In this work, the model of fractional magneto-thermoelasticity is applied to a one-dimensional thermal shock problem for a functionally graded half-space whose surface is assumed to be traction free and subjected to an arbitrary thermal loading. The Lam,'s modulii is taken as functions of the vertical distance from the surface of thermoelastic perfect conducting medium in the presence of a uniform magnetic field. Laplace transform and the perturbation techniques are used to derive the solution in the Laplace transform domain. Numerical inversion of the Laplace transform is carried out to obtain the temperature, displacement, stress and induced magnetic and electric field distributions. Numerical results are represented graphically and discussed.