The present investigation is concerned with the reflection and transmission at elastic half-space and a two-temperature generalized thermoelastic half-space with fractional order derivative. The governing equations in the context of the theory of two-temperature generalized thermoelasticity using the methodology of fractional calculus are used to investigate the problem. The incident wave is assumed to be striking at the plane interface after propagating through the elastic solid half-space. It is found that the amplitude ratios of various reflected and refracted waves are functions of the angle of incidence and frequency of the incident wave. These amplitude ratios are influenced by the fractional-order thermoelastic properties of media. The expressions of amplitude ratios and energy ratios have been computed numerically for a particular model. The variations of energy ratios with the angle of incidence are shown graphically. The conservation of energy at the interface is verified.