  In this work, we establish the maximal $\ell^p$-regularity for several time
stepping schemes for a fractional evolution model, which involves a fractional
derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time. These schemes
include convolution quadratures generated by backward Euler method and
second-order backward difference formula, the L1 scheme, explicit Euler method
and a fractional variant of the Crank-Nicolson method. The main tools for the
analysis include operator-valued Fourier multiplier theorem due to Weis [48]
and its discrete analogue due to Blunck [10]. These results generalize the
corresponding results for parabolic problems.
