In this study, the porous thermoelastic behavior in a half-space microstretch elastic media enveloped in an unbounded inviscid liquid with rotation using memory-dependent derivative, utilizing Green–Naghdi theory mode III (G-N III) and the three-phase-lag model (3PHL). The analytical technique used to obtain the ordinary differential equations was normal mode analysis, followed by elimination of six ordinary differential equations, and finally the characteristic equation to obtain the exact formula of the physical quantities. A Gauthier composite element is employed in an implementation to start comparing the observations rotating on thermo-microstretch elastic porous medium employing a memory-dependent derivative completely covered in the endless fluid of G-N III theory with those for the model of 3PHL.