  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.
