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

Abstract: 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 Friedmann equations in the framework of teleparallel gravity by vierbein field. We consider that Universe dominates by components of cold matter, dark energy and modified Chaplygin gas. In what follows we separately write the corresponding continuity equations for components of Universe. Also, dark energy EoS and effective EoS are obtained with respect to redshift, thereafter the corresponding 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.