The main concern of this article is to discuss the problem of a two-temperature fiber-reinforced micropolar thermoelastic medium with voids under the effect rotation, mechanical force in the context four different theories with memorydependent derivative (MDD) and variable thermal conductivity. The three-phase-lag model (3PHL), dual-phase-lag model (DPL), Green-Naghdi theory (G-N II, G-N III), coupled theory, and the Lord˗Shulman theory (L-S) are employed to solve the present problem. Analytical expressions of the physical quantities are obtained by using Laplace-Fourier transforms technique. Numerical results are shown graphically and the results obtained are analyzed. The most significant points are highlighted