Mathematical Analysis of Coupled Fractional Thermoelastic Semiconductor Equations Under Rotation: A Comparative Study of LST, DPLM, and RDPLM

This paper investigates the impact of rotation on the propagation of coupled thermomechanical waves in a semiconductor thermoelastic medium using a β-fractional derivative model. The research is conducted using three thermoelastic frameworks: the refined dual-phase-lag model (RDPLM), the dual-phase-lag model (DPLM), and the Lord–Shulman theory (LST). The governing equations for heat conduction, elastic deformation, and carrier density are fully connected to accommodate finite-speed heat transport and semiconductor carrier phenomena. To facilitate the analysis, the equations are shown in nondimensional form, and a transformation method is employed to turn the coupled partial differential equations into ordinary differential equations appropriate for analytical solution. The displacement, temperature, carrier density, and stress component solutions are determined, allowing for the investigation of wave propagation inside the medium. Numerical results and graphical demonstrations are used to compare the physical fields with and without rotation across the three models. In semiconductor thermoelastic materials, rotation and the fractional parameter β significantly affect wave propagation characteristics as velocity, amplitude, and attenuation. Among the three theories studied, the RDPLM consistently produced the most stable and physically realistic results, effectively suppressing nonphysical oscillations and exaggerated reactions that could arise in the DPLM and LST.