Distributed-order time-fractional wave equations

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