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In this paper, the model of interaction is studied between $f(T,\mathcal{T})$gravity and modified Chaplygin gas in FRW-flat metric. We obtain the Friedmannequations in the framework of teleparallel gravity by vierbein field. Weconsider that Universe dominates by components of cold matter, dark energy andmodified Chaplygin gas. In what follows we separately write the correspondingcontinuity equations for components of Universe. Also, dark energy EoS andeffective EoS are obtained with respect to redshift, thereafter thecorresponding cosmological parameters are plotted in terms of redshift,thereinafter the accelerated expansion of the Universe is investigated.Finally, the stability of the model is discussed in phase plane analysis.

Stability and interacting $f(T,\mathcal{T})$ gravity with modified Chaplygin gas