Unified fractional derivative models of magneto-thermo-viscoelasticity theory

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 thermoviscoelasticity can be easily obtained. The new fractional model is applied to a halfspace 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.