Fractional Three-Phase-Lag Thermoelastic Analysis of Rayleigh-Wave Propagation in a Nonlocal Semiconductor Half-Space Subjected to Hydrostatic Prestress and Femtosecond Laser Excitation

The study develops a unified fractional-order three-phase-lag theory of thermoelasticity governing Rayleigh wave propagation in a semiconductor half-space experiencing hydrostatic prestress and femtosecond laser heating. Using Caputo fractional derivatives, Eringen’s nonlocal elasticity, electron-hole plasma behavior, and thermal–plasma coupling effects, the normal-mode approach provides the secular equation as well as metrics such as phase velocity, attenuation coefficient, penetration depth, and specific heat loss. Limiting cases show good agreement with the integer-order three-phase-lag, dual-phase-lag, Green-Naghdi Type III, Lord-Shulman, and classical heat conduction models. The main result: the nonlocal parameter accounts for 58% of the sensitivity of the attenuation coefficient, 65% for the penetration depth, and 64% for the specific heat loss. Rotational frequency and hydrostatic stress account for 23% of the sensitivity of the phase velocity each, while the thermal relaxation times make up less than 1%. Therefore, a simple factor-fixing scheme can be used in computations. This work identifies major control parameters for applications to filters, delay lines, micro/nano-mechanical systems, and laser-ultrasonic detection.