On the Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < nu < 2 and give a probabilistic interpretation of its solution. In the case 0 < nu < 1, d = 1, the solution can be interpreted as a time-changed Brownian motion, while for 1 < nu < 2 it coincides with the density of a symmetric stable process of order 2/nu. We give here an interpretation of the fractional wave equation ford >1 in terms of laws of stable d-dimensional processes. We give a hint at the case of a fractional wave equation for nu > 2 and also at space-time fractional wave equations.