Linking multiple relaxation, power-law attenuation, and fractional wave equations

2011 ◽  
Vol 130 (5) ◽  
pp. 3038-3045 ◽  
Author(s):  
Sven Peter Näsholm ◽  
Sverre Holm
Keyword(s):  
Power Law ◽  
Wave Equations ◽  
Fractional Wave Equations

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

scholarly journals Attenuated Fractional Wave Equations With Anisotropy

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Mark M. Meerschaert ◽  
Robert J. McGough
Keyword(s):  
Wave Propagation ◽  
Fractional Calculus ◽  
Power Law ◽  
Wave Equations ◽  
Anomalous Dispersion ◽  
Complex Media ◽  
Attenuation Index ◽  
Fractional Wave Equations ◽  
Analytical Expressions

This paper develops new fractional calculus models for wave propagation. These models permit a different attenuation index in each coordinate to fully capture the anisotropic nature of wave propagation in complex media. Analytical expressions that describe power law attenuation and anomalous dispersion in each direction are derived for these fractional calculus models.

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