This research is devoted to the study of plane wave propagation in homogeneous transversely isotropic magnetothermoelastic rotating medium with combined effect of hall current and two temperature. The research is applied to fractional order theory with three-phase lag heat transfer. It is analysed that, for 2-D assumed model, three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) are present. The wave characteristics like phase velocity, specific loss, attenuation coefficients, energy ratios, penetration depths and amplitude ratios of transmitted and reflected waves are computed numerically and illustrated graphically. The impact of hall current parameter by taking different values is represented graphically. Some particular cases are also derived from this research.