Invariant Bianchi type I cosmological models and conservation laws in f (R, T)=f1(R)+f2(R)f3(T) gravity

f (R, T) theory of gravity can explain the dark energy and the observed late time acceleration of the universe even without cosmological constant. It passes the solar system test and appears to be an alternative of dark matter. We obtain the accelerating solutions of Einstein's field equations, corresponding to Bianchi I spacetime with perfect fluid, in f (R, T) gravity theory without shear. The non-static non-degenerating indefinite smooth solutions of field equations are derived by considering f (R, T) = f1(R) + f2(R)f3(T) with non-minimal matter-geometry coupling. The classical Lie symmetry method is used for symmetry reduction of field equations and for obtaining the exact solutions in terms of arbitrary functions. The graphical representations of solutions are shown by considering the possibilities of arbitrary functions. The conservation laws of Einstein's equations in f (R, T) gravity are also obtained. & COPY; 2023 Elsevier B.V. All rights reserved.