 03120 W. Chen and S. Holm
 Physical interpretation of fractional diffusionwave equation via lossy media obeying frequency power law
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Mar 17, 03

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Abstract. The fractional diffusionwave equation (FDWE)1,2 is a recent generalization of diffusion and wave equations via time and space fractional derivatives. The equation underlies Levy random walk and fractional Brownian motion2,3 and is foremost important in mathematical physics for such multidisciplinary applications as in finance, computational biology, acoustics, just to mention a few. Although the FDWE has been found to reflect anomalous energy dissipations4,5, the physical significance of the equation has not been clearly explained in this regard. Here the attempt is made to interpret the FDWE via a new timespace fractional derivative wave equation which models frequencydependent dissipations observed in such complex phenomena as acoustic wave propagating through human tissues, sediments, and rock layers. Accordingly, we find a new bound (inequality (6) further below) on the orders of time and space derivatives of the FDWE, which indicates the socalled subdiffusion process contradicts the real world frequency power law dissipation. This study also shows that the standard approach, albeit mathematically plausible, is physically inappropriate to derive the normal diffusion equation from the damped wave equation, also known as Telegrapher s equation.
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