  Intense flares that occur at late times relative to the prompt phase have
been observed by the $Swift$ satellite in the X-ray afterglows of gamma-ray
bursts (GRBs). Here, we present a detailed analysis on the fall back accretion
process to explain the intense flare phase in the very early X-ray afterglow
light curves. To reproduce the afterglow at late times, we resort to the
external shock by engaging energy injections. By applying our model to GRBs
080810, 081028 and 091029, we show that their X-ray afterglow light curves can
be reproduced well. We then apply our model to the ultra-long $Swift$ GRB
111209A, which is the longest burst ever observed. The very early X-ray
afterglow of GRB 111209A showed many interesting features, such as a
significant bump observed at around 2000 s after the $Swift$/BAT trigger. We
assume two constant energy injection processes in our model. These can explain
the observed plateau at X-ray wavelength in the relatively early stage
($8.0\times10^{3}$ s) and a second X-ray plateau and optical rebrightening at
about $10^{5}$ s. Our analysis supports the scenario that a significant amount
of material may fall back toward the central engine after the prompt phase,
causing an enhanced and long lived mass accretion rate powering a
Poynting-flux-dominated outflow.
