  We present a measurement of the energy spectrum of ultra-high-energy cosmic
rays performed by the Telescope Array experiment using monocular observations
from its two new FADC-based fluorescence detectors. After a short description
of the experiment, we describe the data analysis and event reconstruction
procedures. Since the aperture of the experiment must be calculated by Monte
Carlo simulation, we describe this calculation and the comparisons of simulated
and real data used to verify the validity of the aperture calculation. Finally,
we present the energy spectrum calculated from the merged monocular data sets
of the two FADC-based detectors, and also the combination of this merged
spectrum with an independent, previously published monocular spectrum
measurement performed by Telescope Array's third fluorescence detector
(Abu-Zayyad {\it et al.}, {Astropart. Phys.} 39 (2012), 109). This combined
spectrum corroborates the recently published Telescope Array surface detector
spectrum (Abu-Zayyad {\it et al.}, {Astrophys. Journ.} 768 (2013), L1) with
independent systematic uncertainties.
