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.