Dynamics of Anisotropic Bianchi type-III Universe within the framework of <i>f</i> ( <i>Q</i> ) gravity

In this work, we examine the exact solutions in an anisotropic Bianchi type-III universe in modified [Formula: see text] gravity. Methods: We consider the specific form of function [Formula: see text] and adopt a hybrid scale factor [Formula: see text] to solve exactly the field equations. By using graphical analysis, we explore the behavior of some important cosmological parameters such as the Hubble parameter, deceleration parameter, equation of state parameter, skewness parameters, energy conditions, and statefinder parameters. Findings: Our result show that the model moves smoothly from an early decelerating phase ([Formula: see text]) to a late-time accelerating phase ([Formula: see text]). The equation of state parameter shifts from zero, which is typical for matter-dominated behavior, to negative values, a clear sign that dark energy becomes more dominant as the universe ages. The strong energy condition is violated from the very beginning, which fits well with current observations of cosmic acceleration. The skewness parameters remain negative throughout, indicating that the dark energy fluid retains its anisotropic nature at all times. The statefinder parameters start in the quintessence region ([Formula: see text]) and eventually approach the [Formula: see text]CDM fixed point ([Formula: see text]) at later times. Novelty: This study explores the universe’s evolution within the framework of [Formula: see text] gravity using a Bianchi type-III anisotropic background with a hybrid scale factor. The strong energy condition is violated, and the equation of state parameter stays negative, both of which match what recent observations tell us about the universe. This gives us deeper insight into why the universe is expanding faster and faster.