In this paper, three-phase lag heat transfer model Roychoudhari  is employed to study the problem of reflection and transmission of thermoelastic waves of an obliquely incident plane P or SV wave at the interface between an elastic solid and a fractional order thermoelastic solid subjected to continues boundary conditions. The amplitude reflection and amplitude transmission coefficients are derived by using the potential method. It was found that the energy ratios and amplitude ratios of waves depend upon the incident angle and the frequency of the incident wave. The problem is illustrated by computing numerical values of amplitude ratios and energy ratios for the copper material. Graphical results for two-phase lag are compared with the corresponding results for three-phase lag theory of thermoelasticity. The effect of fractional order on the energy ratios is also discussed graphically. The present derivation is used to study the energy conservation among the incident, reflected, and transmitted waves. It is verified that in this process there is no energy dissipation at the interface.