A Fractional Acoustic Wave Equation from Multiple Relaxation Loss and   Conservation Laws
  This work concerns causal acoustical wave equations which imply frequency power-law attenuation. A connection between the five-parameter fractional Zener wave equation, which is derived from a fractional stress-strain relation plus conservations of mass and momentum, and the physically well established multiple relaxation framework is developed. It is shown that for a certain continuous distribution of relaxation mechanisms, the two descriptions are equal. 
Sven Peter N\"asholm and Sverre Holm
math-ph math.MP