Investigation of Initial Stress‐Influenced M‐Fractional Thermo‐Elastic Waves in Semiconductor Media Under Three Theories

Abstract

This work investigates the influence of initial stress on the propagation of coupled thermo‐mechanical waves in a semiconductor thermoelastic medium utilizing a M$M$ ‐truncated derivative framework. The analysis is performed within three thermoelastic theories: the dual‐phase‐lag (DPL), Lord–Shulman (L–S), and refined dual‐phase‐lag (RDPL) models. The basic equations for heat conduction, elastic deformation, and carrier transport are fully coupled and include both finite thermal wave speed and carrier density influences. After applying a nondimensionalization procedure to simplify the formulation, a transform method reduces the coupled partial deferential equations (PDEs) to solvable ordinary deferential equations (ODEs), yielding solutions for displacement, temperature, carrier concentration, and stress. The numerical graphical results compare the responses with and without initial stress and show that both initial stress and the M$M$ ‐truncated derivative significantly affect wave speed, attenuation, and amplitude, while clarifying the interaction between thermal effects and carrier dynamics in semiconductor media. Among the three theories tested, the RDPL model consistently produces the most stable and physically realistic results, effectively suppressing nonphysical oscillations and exaggerated reactions that may occur in the DPL and L‐S models. These findings shed light on wave behavior in initially stressed semiconductor medium and demonstrate the efficacy of the selected theoretical framework.