So far, models that describe wave propagation in viscoelastic media have been generalized in the fractional framework using real order fractional derivatives. In this talk we propose the use of complex order fractional derivatives for that purpose. We analyze stress-strain constitutive equations involving derivatives of complex order, and discuss mathematical and physical constraints that lead to acceptable models.

This talk is based on joint work with Teodor M. Atanackovic, Stevan Pilipovi\'c andDu\v san Zorica.