  In order to analyze the wave propagation in three-dimensional isotropic and
viscoelastic body, the Cauchy initial value problem on unbounded domain is
considered for the wave equation written as a system of fractional partial
differential equations consisting of equation of motion of three-dimensional
solid body, equation of strain, as well as of the constitutive equation,
obtained by generalizing the classical Hooke's law of three-dimensional
isotropic and elastic body by replacing Lam\'{e} coefficients with the
relaxation moduli to account for different memory kernels corresponding to the
propagation of compressive and shear waves. By the use of the method of
integral transforms, namely Laplace and Fourier transforms, the displacement
field, as a solution of the Cauchy initial value problem, is expressed through
Green's functions corresponding to both compressive and shear wave propagation.
Two approaches are adopted in solving the Cauchy problem: in the first one the
displacement field is expressed through the scalar and vector fields, obtained
as solutions of wave equations which are consequences of decoupling the wave
equation for displacement field, while in the second approach the displacement
field is obtained by the action of the resolvent tensor on the initial
conditions. Fractional anti-Zener and Zener model I$^{{}^{+}}$ID.ID, as well as
fractional Burgers model VII, as representatives of models yielding infinite
and finite wave propagation speed, are used in numerical calculations and
graphical representations of Green's functions and its short and large time
asymptotic behavior.
