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Accelerating cosmological models are constructed in a modified gravity theory dubbed as f (R, T ) gravity at the backdrop of an anisotropic Bianchi type-III universe. f (R, T ) is a function of the Ricci scalar R and the trace T of the energy-momentum tensor and it replaces the Ricci scalar in the Einstein-Hilbert action of General Relativity. The models are constructed for two different ways of modification of the Einstein-Hilbert action. Exact solutions of the field equations are obtained by a novel method of integration. We have explored the behaviour of the cosmic transit from an decelerated phase of expansion to an accelerated phase to get the dynamical features of the universe. Within the formalism of the present work, it is found that, the modification of the Einstein-Hilbert action does not affect the scale factor. However the dynamics of the effective dark energy equation of state is significantly affected.

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This article deals with the study of Bianchi type V cosmological model filled with perfect fluid in the context of f(R, T) gravity. R and T represent the Ricci scalar and trace of the energy–momentum tensor, respectively. The modified Einstein’s field equations are solved under the consideration of hybrid exponential law for two cases of f(R, T). The presented models are shear free.