In this note we analyse the propagation of a small density perturbation in a
one-dimensional compressible fluid by means of fractional calculus modelling,
replacing thus the ordinary time derivative with the Caputo fractional
derivative in the constitutive equations. By doing so, we embrace a vast
phenomenology, including subdiffusive, superdiffusive and also memoryless
processes like classical diffusions. From a mathematical point of view, we
study systems of coupled fractional equations, leading to fractional diffusion
equations or to equations with sequential fractional derivatives. In this
framework we also propose a method to solve partial differential equations with
sequential fractional derivatives by analysing the corresponding coupled system
of equations
