Abstract
A UNIFIED MATHEMATICAL model of fractional magneto-thermo-viscoelasticty for isotropic perfectly conducting media involving fractional relaxation operator is given. Some essential theorems on the linear coupled and generalized theories of thermo-viscoelasticity can be easily obtained. The new fractional model is applied to a half-space subjected to two different forms of time-dependent thermal shock in, the presence of a transverse magnetic field. The Laplace transform techniques are used. Numerical computation is performed by using a numerical inversion technique and the resulting quantities are shown graphically. The effects of the fractional orders on viscoelastic material are discussed.