scholarly journals Time-domain comparisons of power law attenuation in causal and noncausal time-fractional wave equations

2016 ◽  
Vol 139 (5) ◽  
pp. 3021-3031 ◽  
Author(s):  
Xiaofeng Zhao ◽  
Robert J. McGough
Keyword(s):  
Power Law ◽  
Time Domain ◽  
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].

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