Abstract
A mathematical model of magneto electro-thermoelasticity has been constructed in the context of a new consideration of fractional Green-Naghdi heat conduction law without energy dissipation. The governing coupled equations are applied to a one-dimensional problem for a perfect conducting spherical cavity subjected to an arbitrary thermal shock in the presence of a uniform magnetic field. By means of the Laplace transform and numerical Laplace inversion, the problems are solved. The distributions of the considered temperature, stress and displacement are represented graphically. Some comparisons are shown in the figures to estimate the effects of the fractional order and relaxation time.