On the Rayleigh surface wave dynamics of porous piezo-thermoelectric smart material with spatio-temporal nonlocality and fractional higher-order three-phase-lag theory

This study examines Rayleigh-type surface wave propagation in a porous piezo-thermoelectric semi-infinite medium incorporating spatio–temporal nonlocality together with fractional higher-order three-phase-lag heat conduction. The governing equations are formulated within the framework of porosity-dependent thermoelasticity and solved analytically using the wave-mode approach under traction-free boundary conditions. Numerical analysis is carried out to investigate the effects of nonlocal parameters, fractional order, thermal relaxation times, and porosity on phase velocity, attenuation, and particle motion. The results demonstrate that spatio–temporal nonlocal interactions and fractional thermal memory significantly influence wave dispersion and energy dissipation compared to classical thermoelastic models. Several existing theories are recovered as limiting cases, confirming the generality of the formulation. The study provides a useful framework for understanding wave behavior in porous piezo-thermoelectric materials relevant to sensing and surface acoustic wave device applications.