  In this paper, we consider the finite difference method for the generalized
two-dimensional (2D) multi-term time-fractional Oldroyd-B fluid model, which is
a subclass of non-Newtonian fluids. Different from the general multi-term time
fractional equations, the generalized fluid equation not only has a multi-term
time derivative but also possess a special time fractional operator on the
spatial derivative. Firstly, a new discretization of the time fractional
derivative is given. And a vital lemma, which plays an important role in the
proof of stability, is firstly proposed. Then the new finite difference scheme
is constructed. Next, the unique solvability, unconditional stability, and
convergence of the proposed scheme are proved by the energy method. Numerical
examples are given to verify the numerical accuracy and efficiency of the
numerical scheme as compared to theoretical analysis, and this numerical method
can be extended to solve other non-Newtonian fluid models.
