  Distributed-order time-fractional wave equations appear in the modeling of
wave propagation in viscoelastic media. The material characteristics of the
medium are modeled through constitutive functions or distributions in the
distributed-order constitutive law. In this work we propose to take positive
Radon measures for the constitutive "functions".
  First, we derive a thermodynamical restriction on the constitutive measures
which is easy to check, and therefore suitable for applications. Then we prove
that the setting with measures in combination with the derived thermodynamical
restriction guarantee existence and uniqueness of solutions for the
distributed-order fractional wave equation. We further discuss the support and
regularity of the fundamental solution, and conclude with a discussion on wave
velocities.
