Abstract
The new model of the equations of the linear theory of magneto-thermo-viscoelasticity with two relaxation times and fractional heat transfer involving fractional relaxation operator is given. The resulting formulation is applied to thermal shock problems for a perfect electrically conducting half-space in the presence of a transverse magnetic field. Laplace transform techniques are used. Some essential theorems on the linear coupled and generalized theories of thermo-viscoelasticity with two relaxation times are established. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The effects of the fractional relaxation operator on viscoelastic material like poly (methyl methacrylate) (Perspex) are discussed.