  We report three new FRBs discovered by the Five-hundred-meter Aperture
Spherical radio Telescope (FAST), namely FRB 181017.J0036+11, FRB 181118 and
FRB 181130, through the Commensal Radio Astronomy FAST Survey (CRAFTS).
Together with FRB 181123 that was reported earlier, all four FAST-discovered
FRBs share the same characteristics of low fluence ($\leq$0.2 Jy ms) and high
dispersion measure (DM, $>1000$ \dmu), consistent with the anti-correlation
between DM and fluence of the entire FRB population. FRB 181118 and FRB 181130
exhibit band-limited features. FRB 181130 is prominently scattered
($\tau_s\simeq8$ ms) at 1.25 GHz. FRB 181017.J0036+11 has full-bandwidth
emission with a fluence of 0.042 Jy ms, which is one of the faintest FRB
sources detected so far. CRAFTS starts to built a new sample of FRBs that fills
the region for more distant and fainter FRBs in the fluence-$\rm DM_E$ diagram,
previously out of reach of other surveys. The implied all sky event rate of
FRBs is $1.24^{+1.94}_{-0.90} \times 10^5$ sky$^{-1}$ day$^{-1}$ at the $95\%$
confidence interval above 0.0146 Jy ms. We also demonstrate here that the
probability density function of CRAFTS FRB detections is sensitive to the
assumed intrinsic FRB luminosity function and cosmological evolution, which may
be further constrained with more discoveries.
