The development of disturbances of arbitrary shape propagating in a pipe was formulated. The disturbances were divided into two types and discussed independently ; one exhibits normal dissipation, and the other, an anomalous one. Governing equations for the two types of disturbances were derived and solved analytically. The equations include Weyl and Riemann-Liouville fractional derivatives, respectively, for the disturbance with normal dissipation and that with an anomalous one. It was found that the two types of disturbance both have a global nature which is quite different from each other especially near the wavefront.
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