Fractional diffusion and wave equations

DOI PDF 被引用文献3件
  • W. R. Schneider
    Asea Brown Boveri Corporate Research, CH-5405 Baden, Switzerland
  • W. Wyss
    Department of Physics, University of Colorado, Boulder, Colorado 80309

書誌事項

公開日
1989-01-01
DOI
  • 10.1063/1.528578
公開者
AIP Publishing

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説明

<jats:p>Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with tα−1/Γ(α), α=1,2, respectively. Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green’s functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown that the Green’s function of fractional diffusion is a probability density.</jats:p>

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