Fractional-Hyperbolic Systems

We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (0,1)$inthetimevariable$t$ and the first order derivatives in spatial variables $x=(x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n)$, 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 $\{(t,x):\mathrm{\mid }{t}^{-\alpha }x\mathrm{\mid }\le 1\}$.