LAUSR

This study conducts a comprehensive comparative analysis of two influential cosmological theories, namely Brans–Dicke and [Formula: see text] theory of gravity, within the context of a new form of the deceleration parameter, i.e. Fractional Quadratic Deceleration Parameter. This investigation explores the unique features and intrinsic beauty of each theory, highlighting the adaptability of Brans–Dicke with its scalar field and the importance of [Formula: see text] through its modified geometric interactions. The new form of the deceleration parameter i.e. [Formula: see text] serves as a catalyst for redefining our understanding of cosmic dynamics. Precautions have been taken to ensure the robustness of the comparison, including the consideration of model dependence, numerical stability, and sensitivity analysis.