  This paper aims to investigate the possibility of physically achievable new
wormhole solutions within the context of Finsler geometry by focusing on
conformal motion. For this purpose, we study the barotropic linear equation of
state (EoS). We scrutinized their geometric features within the EoS model,
which includes baryonic and non-baryonic matter. Through derived field
equations, shape functions adhering to critical criteria governed by the
Finsler parameter $\gamma$ are explored. By evaluating energy conditions,
violations are found, which indicate the potential presence of exotic matter
necessary for traversable wormholes. Notably, violations of energy conditions
signify the plausibility of traversable wormholes within the conformally
transformed Finslerian space observed in both baryonic and non-baryonic
scenarios. Additionally, anisotropy exploration uncovers repulsive geometric
characteristics within these wormholes.
