Purpose <p>This study presents a fractional three-phase-lag (TPL) thermoelastic model incorporating the Atangana-Baleanu (AB) fractional derivative for analyzing the thermoelastic behaviour of porous solids.</p> Methods <p>The governing constitutive relations are first established, and the resulting partial differential equations are transformed into a system of ordinary differential equations via the Laplace transform. These are solved through the vector-matrix differential equation method, while the Stehfest scheme is employed to numerically invert the Laplace transform and obtain the time-domain solutions.</p> Results <p>Numerical simulations are conducted, and comparative analyses are performed for two different boundary conditions (pulse and ramp-type heating) as well as against other thermoelastic theories, including the Green-Naghdi type III, Dual-Phase-Lag, and Lord-Shulman. The results reveal that fractional order parameters, porosity, and boundary conditions significantly influence thermal attenuation and stress distribution. Moreover, the non-singular Mittag-Leffler kernel associated with the AB derivative effectively captures memory effects and non-Fourier heat conduction behavior.</p> Conclusion <p>The proposed model aligns well with existing results, confirming its reliability and applicability for studying advanced porous thermoelastic materials in engineering contexts.</p>