Modified Szabo's wave equation models for lossy media obeying frequency power law

Details Modified Szabo's wave equation models for lossy media obeying frequency power law Modified Szabo's wave equation models for lossy media obeying frequency power law

2002-12-30

arxiv.org/abs/math-ph/0212076v1

Physics

Mathematical Physics

Scientific paper

10.1121/1.1621392

Szabo's models of acoustic attenuation (Szabo 1994a) comply well with the empirical frequency power law involving non-integer and odd integer exponent coefficients while guaranteering causality, but nevertheless encounter the troublesome issues of hyper-singular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ease or remove these drawbacks of the Szabo's models via the Caputo fractional derivative concept. The positive time fractional derivative is also first introduced to include the positivity of the attenuation possesses.

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