<p>The problem of an infinitely long solid bi-layered cylinder composed of two different conducting materials is considered within the context of the fractional-order theory of thermoelasticity. In the presence of a constant magnetic field, the cylinder is composed of a solid cylinder surrounded by a thick cylindrical shell of different material whose lateral surface is traction-free and subjected to laser pulses. A direct approach and Laplace transform techniques are used to derive the solution in a transformed domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the results are carried out and represented graphically. The application of the magnetic field to cylindrical shapes is very important because it is always present in the production of machine components. The results show the effect of fractional parameter α on the speed of waves. The effect of the time duration of a laser pulse <i>t</i>_<i>p</i> is noted on all distributions. The applied magnetic field H₀ has a very weak effect on the temperature and displacement but has a noticeable effect on the stresses. The result provides an impetus for the investigation of thermoelastic materials as a new class of applicable materials.</p>