On the Rayleigh-Stokes problem for generalized fractional Oldroyd-B fluids

Abstract

We consider the initial-boundary value problem for the velocity distribution of a unidirectional flow of a generalized Oldroyd-B fluid with fractional derivative model. It involves two different Riemann-Liouville fractional derivatives in time. The problem is studied in a general abstract setting, based on a reformulation as a Volterra integral equation with kernel represented in terms of Mittag-Leffler functions. Special attention is paid to the solution behavior in the scalar case, using some facts of the theory of the Bernstein functions. Numerical experiments are performed for different values of the parameters and plots are presented and discussed. The results are compared to those obtained in the limiting cases of generalized fractional Maxwell and second grade fluids.