  This work investigates the effect of phonon coupling on the transfer of
population and creation of coherence using variant of stimulated Raman
adiabatic passage (STIRAP) known as \emph{fractional} stimulated Raman
adiabatic passage (FSTIRAP). The study is based on the Liouville equation,
which is solved numerically in the adiabatic limit. Although the phonon is
assumed to be coupled only to the intermediate state, it is coupled to the
other two states by dipolar system-environment interaction, inducing phonon
coupling to the other states which are not directly in contact with the phonon.
At zero temperature the STIRAP pulse protocol's efficiency of the transfer
decreases exponentially with the electron-phonon coupling, until the coupling
strength is strong enough to make the process fully incoherent, in which case
the population transfer is $\frac{1}{3}$ in each level. For the FSTIRAP
protocol we find that the transferred population to target state decreases,
leaving some population on the intermediate state. Consequently, there is an
increase in the magnitude of the coherences $\rho_{01}, \rho_{12}$, albeit
small. Furthermore population transfer for non-zero temperature and effect of
coupling strength is investigated, it is observed that while both parameters
negatively influence the efficiency of transfer the former decrease the
transfer exponentially, thereby equilibrating the system fast, while the latter
seen to decrease the transfer monotonically, and hence equilibrates slowly.
