Fractional Lord–Shulman Modeling of Photothermoelastic Carrier Dynamics in a Fiber-Reinforced Anisotropic Semiconductor Half-Space with Magnetic and Gravity Coupling

This study develops a fractional Lord–Shulman thermoelastic formulation for coupled photothermoelastic carrier dynamics in a fiber-reinforced anisotropic semiconductor half-space with magnetic and gravity coupling. The governing thermal, elastic, carrier diffusion, and electromagnetic equations are reduced by a normal mode/state-space procedure and solved semi-analytically: the field reduction is analytical, whereas the admissible eigenvalues and boundary constants are evaluated computationally. A Caputo time-fractional operator represents hereditary thermal transport, and the formulation recovers the integer-order Lord–Shulman model at β = 1 and the Fourier/CTE limit when the relaxation term is removed. The available numerical illustrations focus on fractional-order sensitivity, the CTE/Lord–Shulman comparison, and the mechanical influence of reinforcement. The legacy figure set does not independently sweep gravity, magnetic field strength, or optical amplitude; consequently, those quantities are treated as model couplings rather than demonstrated parametric effects in the present revision. The carrier field is comparatively insensitive to the fractional order in the displayed profiles, whereas the mechanical fields show stronger changes. The revised formulation also provides explicit notation, scaling, and symbolic state-space checks required for a reproducible final numerical rerun.