Fractional-Hyperbolic Systems

Abstract

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 $\{(t,x):|t^{-\alpha }x|\le 1\}$.

Final version. available at http://link.springer.com/journal/13540

References in corpus (1)

• Propagation Speed of the Maximum of the Fundamental Solution to the Fractional Diffusion-Wave Equation