  In this paper, we have investigated some features of anisotropic accelerating
Bianchi type-I cosmological model in the presence of two non-interacting
fluids, i.e. one usual string and other dark energy fluid towards the
gravitational field equations for the linear form of $f(T)$ gravity, where
\textit{T }be the torsion. To achieve a physically realistic solution of the
field equations, we have considered an exact matter dominated volumetric power
law expansion. The aspects of derived model are discussed with the help of
solution and make the model at late times turn out to be flat Universe. Also,
observed that the model has initially non-singular and stable while for whole
expansion it is unstable. At an initial expansion $0.01\le t\le 0.05$ when the
Universe start to expand to infinite expansion $t>1.73$ (break away from for
small interval of cosmic time $0.06\le t\le 1.73$), there is a matter dominated
era while for $0.06\le t\le 1.73$ it approaches the quintessence region. Also,
the string exists in the early universe which is in agreement with constraints
of CMBR data but with the expansion the string phase of the Universe
disappears, i.e. we have an anisotropic fluid of particles.
