  The geodesic deviation equation has been investigated in the framework of
$f(T,\mathcal{T})$ gravity, where $T$ denotes the torsion and $\mathcal{T}$ is
the trace of the energy-momentum tensor, respectively. The FRW metric is
assumed and the geodesic deviation equation has been established following the
General Relativity approach in the first hand and secondly, by a direct method
using the modified Friedmann equations. Via fundamental observers and null
vector fields with FRW background, we have generalized the Raychaudhuri
equation and the Mattig relation in $f(T,\mathcal{T})$ gravity. Furthermore, we
have numerically solved the geodesic deviation equation for null vector fields
by considering a particular form of $f(T,\mathcal{T})$ which induces
interesting results susceptible to be tested with observational data.
