Fractional calculus is a powerful tool for modeling phenomena arising in diverse

fields of science such as mechanics, physics, engineering, economics, finance,

medicine, biology, chemistry, etc. It deals with derivatives and integrals of arbitrary

real (or even complex) order, and thus extend the capabilities of the classical

calculus. For instance, fractional derivatives more accurately describe properties

of viscoelastic materials than the integer order ones. This is of particular

interest for the study of wave propagation in viscoelastic media.

We present various generalizations of the wave equation within the

framework of fractional calculus. The approach is based on different

possibilities for fractionalization (i.e., substitution of the integer order

derivatives with the fractional ones) of the stress-strain constitutive

equation in the model of wave propagation in elastic media,

with the aim of preserving the physical meaning of the model.

This talk is based on joint work with T. M. Atanackovic,

S. Pilipovic, Lj. Oparnica and D. Zorica.