The effects of fractional derivative and gravity on wave propagation in micro-elongated thermo-elastic media under the refined dual-phase-lag model

This paper examines the impact of gravity on wave propagation in a micro-elongated thermoelastic medium incorporating fractional conformable derivatives under the Dual-Phase-Lag (DPL) and the Refined Dual-Phase-Lag (RDPL) model. The governing equations of heat conduction, motion, and microelongation are formulated to account for finite thermal propagation speed, microelongated, and gravitational effects. By implementing a suitable nondimensionalization process and applying the Normal Mode Analysis method, the coupled system of partial differential equations is reduced to an semi-analytically solvable. Solutions for displacement, stress, temperature, and microelongation fields are obtained, enabling a detailed assessment of the dynamic response of the medium. Numerical simulations are performed to illustrate the role of fractional-order parameters and phase-lag effects in modifying wave characteristics. The results demonstrate that gravity has a significant impact on wave amplitude, velocity, and attenuation, while the fractional conformable derivative and RDPL model enhance control over thermal relaxation behavior. This study contributes to improved modeling of advanced thermoelastic materials in gravitational environments.