Abstract. This study aims a comprehensive investigation of the Bianchi-III cosmological model, within the framework of Brans-Dicke theory (BDT) of gravity. The uniqueness of our approach lies in the incorporation of a fractional linear varying deceleration parameter (FLVDP), denoted as q(t) = (ξ1 - ξ2t)/(1 + ξ2t). This innovative parameter allows us to study the evolving behavior of the universe's expansion. Our primary objective is to derive solutions to the Einstein field equations (EFE) within this distinctive framework. These solutions form the basis for understanding how the universe's geometry and dynamics evolve over cosmic time. Additionally, we have studied the physical and geometric characteristics of cosmological model. Utilizing graphical representations, we offer visual insights into various model parameters, facilitating the interpretation of the universe's complex behavior.

doi: https://doi.org/10.55318/bgjp.2025.52.3.237

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