Wave propagation and some basic theorems like variational principle, uniqueness theorem, and theorem of reciprocity are studied for an anisotropic piezothermoelastic solid with two-temperature and fractional order derivative. The basic governing equations are used to study the interesting problem. Also, we characterize an alternative formulation of the mixed initial boundary value problem. These theorems are also summarised for a special case of orthotropic piezothermoelastic solid with the consideration of two-temperature theory and fractional order derivative. The non-trivial solution of the system is insured by a quartic equation whose roots represent the complex velocities of four attenuating waves in the medium. The different characteristics of the waves like phase velocity and attenuation quality factor are plotted three-dimensionally with the change in direction for two different models. Some special cases are also deduced from the present investigation.