<p>This paper presents a comprehensive study of the fluid pressure distribution in a fractured porous medium, taking into account fluid flow through both fractures and matrix blocks. The intricate flow patterns induced by porous networks in the medium result in unusual behavior in flow characteristics. The fractional Darcy’s law is considered to address the type of ambiguity present in these scenarios. Accounting for this, a system of fractional differential equations describing the fluid flow through a fractured medium is developed, and the existence and uniqueness of its solution are discussed. To validate the model and investigate the solution behavior, two independent numerical methods are developed and analyzed: an unconditionally stable finite difference scheme and a spectral method based on fractional Jacobi functions that yields a closed-form polynomial approximation. Convergence analysis for the spectral scheme is carried out, and stability is examined for the finite difference method. The characteristic of the solution is found to depend strongly on the permeability ratio between the matrix and fracture domains, as well as on the order of the fractional derivative. The interplay between medium permeability, fractional derivative order, and the resulting pressure distribution is examined in detail.</p>