  We describe a class of evolution systems of linear partial differential
equations with the Caputo-Dzhrbashyan fractional derivative of order $\alpha
\in (0,1)$ in the time variable $t$ and the first order derivatives in spatial
variables $x=(x_1,...,x_n)$, which can be considered as a fractional analogue
of the class of hyperbolic systems. For such systems, we construct a
fundamental solution of the Cauchy problem having exponential decay outside the
fractional light cone $\{(t,x):\ |t^{-\alpha}x|\le 1\}$.
