Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency

2004 ◽  
Vol 115 (4) ◽  
pp. 1424-1430 ◽  
Author(s):  
W. Chen ◽  
S. Holm
Keyword(s):  
Power Law ◽  
Fractional Laplacian ◽  
Time Space ◽  
Lossy Media ◽  
Linear And Nonlinear ◽  
Arbitrary Frequency ◽  
Frequency Power

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Improved description of shock wave evolution in media with frequency power law dependent attenuation

2001 ◽  
Vol 109 (5) ◽  
pp. 2263-2265 ◽  
Author(s):  
Kirk D. Wallace ◽  
Mark R. Holland ◽  
James G. Miller
Keyword(s):  
Shock Wave ◽  
Power Law ◽  
Wave Evolution ◽  
Frequency Power
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