Fractional order theory of a perfect conducting thermoelastic medium

In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is applied to a one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of magnetic field. Laplace transforms and state-space techniques (Ezzat. Can. J. Phys. 86, 1242, (2008)) will be used to obtain the general solution for any set of boundary conditions. According to numerical results and graphs, it is found that introducing a fractional derivative of order alpha has a significant effect on the temperature, stress, and heat flux distributions as well as the induced electric and magnetic fields; the curves are smoother in the case of 0 < alpha < 1 due to weak thermal conductivity. Some comparisons are made and shown in figures to estimate the effects of the fractional order parameter on all the studied fields.