Generalized equations of hydrodynamics for viscoelastic fluids in fractional derivatives

Non-Markov equations of hydrodynamics in fractional derivatives for non-equilibrium values of particle number densities, their momentum, and energy for viscoelastic fluids using the non-equilibrium statistical operator method in Gibbs statistics are obtained. For isothermal processes (β=1/kBT=const), the non-Markov Navier–Stokes equation in fractional derivatives for viscoelastic fluids is obtained. Models of the frequency dependence of the memory function (viscosity) are considered, which lead to a generalized equation in fractional derivatives in space and time for the non-equilibrium value of the particle momentum density (or generalized Navier–Stokes) for the generalized Maxwell fluid model, the generalized Oldroyd B fluid model.