The influence of hydrostatic initial stress in the context of the time-fractional heat order equation is investigated. The strong electromagnetic field is applied at the external surface of semiconductor elastic medium during the photothermal transport process. The Thomson influence appears due to the strong magnetic field. The behavior of wave propagations of the elastic medium is obtained in context of the thermoelectricity theory with initial stress. The governing main equations are taken in two dimensions to describe the interaction between elasticthermal- plasma and electromagnetic waves for fractional cases. The density of charge is studied as a function of time only when the electric current is induced. The separation of variables is used as a mathematical technique to obtain the exact solutions of the distributions of physical quantities under investigation. Some mechanical, thermal, plasma and magnetic conditions are applied at the free surface elastic medium. A numerical simulation is used to obtain physical quantities distributions graphically and discussed theoretically in various fractional cases.