In this scholarly work, a novel mathematical model for single-phase, single-well simulation in hydrocarbon reservoirs was established using the fractional calculus theory. Specifically, the existing fractional generalization of Darcy's law is reconstructed by introducing an auxiliary parameter to ensure that the definition of the conventional rock permeability with dimension L 2 was preserved. Subsequently, the newly constructed fractional flux relationship was substituted as a momentum equation in the mass conservation expression in the radial-cylindrical coordinate system. The resulting nonlocal time-radial diffusivity equation was solved numerically using the block-centered finite-difference approximation and adopting the Grünwald–Letnikov formula for the definition of the fractional-order derivative. The developed numerical scheme was verified by comparing the approximate pressure solution against the semi-analytical solution of the simplified nonlocal time-radial diffusivity equation and the classic radial flow diffusivity equation. Furthermore, incremental material balance checks were performed and exhibited to ensure the conservation of mass at each time step. Finally, a detailed sensitivity analysis was performed to evaluate the impact of the order of fractional differentiation on pressure distribution in the reservoir and wellbore. The proposed nonlocal time-radial diffusivity equation proffers a useful model for single-well simulation in geological media that exhibit distorted flow paths and near power-law behaviors.