With the rapid advancement of materials science and chemical engineering, engineering applications involving complex viscoelastic fluids—such as blood flow, asphalt paving, and colloidal processing—are increasingly prevalent. The traditional Oldroyd-B model remains one of the most classical constitutive models for viscoelastic fluids, yet it exhibits limitations when characterizing fluids with intricate microstructures. Caputo fractional derivatives demonstrate significant advantages in describing the complex rheological properties and long-time memory effects of viscoelastic fluids. Therefore, this study aims to investigate the flow behavior of Caputo fractional Oldroyd-B fluids in a top-driven square cavity through numerical simulation. Based on ANSYS Fluent software and employing the finite volume method, this study coupled the fractional Oldroyd-B fluid constitutive equations with the Navier-Stokes equations through user-defined functions and user-defined scalars. The effects of different fractional-derivative orders, Weissenberg numbers, and Reynolds numbers on flow-field structures, vorticity distributions, and vortex-center locations were investigated. To overcome numerical instability at high Weissenberg numbers, an artificial viscosity term was introduced into the transport equation, drawing on strategies from integer order models. Comparison with benchmark data from existing literature demonstrates good agreement in key metrics such as velocity distribution and vortex center location, validating the accuracy and effectiveness of the numerical model.