The present study provides a comprehensive investigation of traversable wormhole solutions within the framework of Finsler geometry, offering a novel extension beyond conventional Riemannian approaches. By formulating and analyzing a modified gravitational field equation, we establish the fundamental conditions necessary for the stability and traversability of the wormhole. By incorporating a linear equation of state, \(p_r = \gamma \rho\) , alongside a meticulously chosen shape function, we ensure adherence to essential geometric constraints. Through rigorous examination of proper radial distance, active mass, and total gravitational energy, we demonstrate that the Finslerian parameter \(\lambda\) plays a critical role in shaping the wormhole’s physical properties. Notably, our findings reveal that Finslerian effects significantly modify the energy conditions, offering a more viable framework for wormhole existence. Furthermore, we establish that for specific values of \(\lambda\) , the total gravitational energy remains favorable for traversability, while excessive accumulation may trigger black hole formation. In addition to advancing the understanding of Finslerian wormholes in modified gravity theories, this study also underscores their astrophysical significance, paving the way for future explorations in higher-dimensional and anisotropic space-time models.
