  The present work is devoted to investigate the Noether symmetries of the
locally rotationally symmetric Bianchi type I space time in $f(T,B)$ gravity
theory which depends on the torsion scalar $T$ and the boundary term $B$. In
this theory, we consider some particular models and investigate their Noether
symmetry generators. Besides, we get exact cosmological solutions of the
considering models including the matter dominant universe using the Noether
symmetry technique. The obtained results are coincide with the accelerated
expansion behaviour of the universe.
