  In this paper, a general FRW cosmological model has been constructed in
$f(R,T)$ gravity reconstruction with variable cosmological constant. A number
of solutions to the field equations has been generated by utilizing a form for
the Hubble parameter that leads to Berman's law of constant deceleration
parameter $q=m-1$. The possible decelerating and accelerating solutions have
been investigated. For ($q>0$) we get a stable flat decelerating
radiation-dominated universe at $q=1$. For ($q<0$) we get a stable accelerating
solution describing a flat universe with positive energy density and negative
cosmological constant. Nonconventional mechanisms that are expected to address
the late-time acceleration with negative cosmological constant have been
discussed.
