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.
Attenuated Fractional Wave Equations With Anisotropy
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 18, 2013; final manuscript received October 24, 2013; published online July 25, 2014. Assoc. Editor: Thomas J. Royston.
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Meerschaert, M. M., and McGough, R. J. (July 25, 2014). "Attenuated Fractional Wave Equations With Anisotropy." ASME. J. Vib. Acoust. October 2014; 136(5): 050902. https://doi.org/10.1115/1.4025940
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