  \alpha^1 Her is the second closest Asymptotic Giant Branch (AGB) star to the
Sun, and the variable luminous M5 Ib-II member of a triple stellar system
containing G8 III and A9 IV-V components. However, the mass of this important
star was previously uncertain with published values ranging from ~2 - 15 Msun.
As shown by this study, its fortuitous membership in a nearby resolved triple
star system, makes it possible to determine its fundamental properties
including its mass and age. We present over twenty years of VRI photometry of
\alpha^1 Her as well as Wing intermediate-band near-IR TiO and NIR continuum
photometry. We introduce a new photometry-based calibration technique, and
extract the effective temperature and luminosity of \alpha^1 Her, in agreement
with recent interferometric measures. We find, Teff=3280 +/- 87 K and
log(L/Lsun)=3.92 +/- 0.14.
  With the MESA code, we calculate a dense grid of evolutionary tracks for
Galactic low- to intermediate-mass (1.3 to 8 Msun) rotating stars from the
pre-main sequence phase to the advanced AGB phase. We include atomic diffusion
and rotation mechanisms to treat the effects of extra elemental mixing. Based
on the observed properties of the \alpha Herculis stars, we constrain the age
of the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of \alpha^1
Her lies in the range 2.175 <= M/Msun <= 3.250. We compare our model-based age
inference with recent tracks of the Geneva and STAREVOL codes, and show their
agreement. In the prescribed mass range for \alpha^1 Her, the observed 12C/13C
and 16O/17O ratios are consistent (within 2\sigma) with the ratios predicted by
the MESA, Geneva and STAREVOL codes.
