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

DOI10.1121/1.1621392arXivmath-ph/0212076WikidataQ52007390 ScholiaQ52007390MaRDI QIDQ6468836

Publication date: 30 December 2002

Abstract: 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.

Mathematics Subject Classification ID

Wave equation (35L05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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