Bianchi Type Perfect Fluid Cosmological Model in Modified Theory of Gravity

In this work, we investigate a spatially homogeneous and anisotropic BT-[Formula: see text] cosmological model filled with a perfect fluid source in the framework of modified [Formula: see text] gravity. Exact solutions of the nonlinear field equations are obtained by assuming a power-law relation between [Formula: see text] and the average scale factor together with a proportionality condition between the shear and expansion scalars. The obtained model describes a continuously expanding Universe with positive energy density, negative pressure, and a negative deceleration parameter, supporting late-time accelerated expansion. The EoS parameter remains entirely in the phantom region [Formula: see text], while the [Formula: see text] phase-plane analysis exhibits attractor-like behavior. Energy condition analysis shows that the DEC is satisfied, whereas the NEC and SEC are violated, consequently, NEC violation is a sign of exotic phantom behavior arising from modified [Formula: see text] gravity effects, while accelerated expansion results from SEC violation. Perturbative analysis indicates unstable behavior under small fluctuations. Furthermore, observational diagnostics including Hubble evolution, distance modulus show consistency with DA, BAO, [Formula: see text]CDM, and Pantheon datasets. Therefore, the obtained BT-[Formula: see text] framework provides an observationally viable description of late-time accelerated expansion in anisotropic modified gravity cosmology.