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In this paper we explore $f(T, \mathcal{T})$, where $T$ and $\mathcal{T}$denote the torsion scalar and the trace of the energy-momentum tensorrespectively. We impose the covariant conservation to the energy-momentumtensor and obtain a cosmological $f(T, \mathcal{T})$ respectively. We imposethe covariant conservation to the energy-momentum tensor and obtain acosmological $f(T, \mathcal{T})$ model. Then, we study the stability of theobtained model for power-law and de Sitter solutions and our result show thatthe model can be stable for some values of the input parameters, for bothpower-law and de Sitter solutions.

$f(T,\mathcal{T})$ Cosmological Models in Phase Space