Fractional-hyperbolic systems

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• 作者：Anatoly N. Kochubei (1)
  
• 关键词：Primary 35R11 ; 35L99 ; hyperbolic systems ; Caputo ; Dzhrbashyan fractional derivative ; fundamental solution of the Cauchy problem
• 刊名：Fractional Calculus and Applied Analysis
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：16
• 期：4
• 页码：860-873
• 全文大小：
• 作者单位：Anatoly N. Kochubei (1)
  
  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev, 01601, Ukraine
  

文摘

We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order α ∈ (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 -α| ≤ 1}.