  We consider the numerical approximation of a generalized fractional Oldroyd-B
fluid problem involving two Riemann-Liouville fractional derivatives in time.
We establish regularity results for the exact solution which play an important
role in the error analysis. A semidiscrete scheme based on the piecewise linear
Galerkin finite element method in space is analyzed and optimal with respect to
the data regularity error estimates are established. Further, two fully
discrete schemes based on convolution quadrature in time generated by the
backward Euler and the second-order backward difference methods are
investigated and related error estimates for smooth and nonsmooth data are
derived. Numerical experiments are performed with different values of the
problem parameters to illustrate the efficiency of the method and confirm the
theoretical results.
