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 ($tau_ssimeq8$ 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.
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