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Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796–2815 (2000)] is one of the most successful models for wave propagation in fluid-saturated granular sediments. In this paper, I show that the GS model as well as its further improved viscous-GS (VGS) model can be expressed using the mathematical framework of fractional calculus. The fractional version of the standard fluid model is adopted to independently arrive at the equations derived by Buckingham. The fractional wave equations obtained for the compressional waves and shear waves are relatively easier to analyze and appear elegant, than the equations from the VGS model. It is shown that the fractional calculus approach may help in bridging the disparate fields of non-Newtonian rheology and sediment acoustics, which may have actually developed independently of each other. Furthermore, the experimental data relating wave dispersion in marine sediments is curve-fitted to match with the predictions from the fractional framework. The overall goal is to show that fractional calculus is not just a framework that can only be mathematically introduced to curve-fit the observational data. Rather, it has an inherent connection to real physical processes that needs to be explored more.
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