This paper deals with problems for the description of nonlinear planar traveling waves in a gas-filled tube. These waves, which are influenced by the tube-wall boundary layer, can be described by both the Burgers equation and the Khokhlov–Zabolotskaya–Kuznecov’s equation with the inclusion of a hereditary integral known as the fractional derivate of order1/2 . Emphasis is placed on comparison of applicability of both the mentioned equations with respect to experimental data. The applicability of the Burgers model equation is limited by the cutoff frequency of the tube which is exceeded due to the growth of higher harmonic components that is caused by the nonlinear distortion of the primary harmonic shape of waves. The next part of this contribution is dedicated to the presentation of some new approximate solutions of the Burgers equation with a fractional derivate and a brief description of used numerical methods.