  An extension of the time-dependent Hartree-Fock-Bogoliubov theory (ETDHFB)
which includes higher-order effects such as screening of the pairing
correlation is proposed. ETDHFB is applied to a fermion system trapped in a
harmonic potential to test its feasability by comparison with the exact
solution. With the use of perturbative expressions for the pairing tensor and
the two-body density matrix derived from ETDHFB, the screening effect is
investigated for atomic fermion systems and isotopes of tin nuclei. It is found
that the screening effect on the pairing correlation is not significant.
