Abstract. In this study, we have conducted certain investigations of Bianchi-III cosmological models with fractional linear varying deceleration parameter (FLVDP) within the framework of the f(R,T) theory. The aim was to examine the behaviour of the expansion rate of the universe over time. We have assumed deceleration parameter (DP) as q(t) = 1 - α₁t/(1 + α₂t) where α₁, α₂ ≥ 0 and q(t) = - 1 + nβ/(β + t)² where n, β > 0. In this article, we have examined the values of a number of constants that can be used to explain the universe as it moves from an early stage of cosmic deceleration to a later stage of cosmic acceleration. Additionally, physical and graphic behaviours, along with energy conditions and the jerk parameter, have also been explored in this study.

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