In this paper, we suggest a fractional-order susceptible, exposed, infectious, and latent (SEIL) epidemic model with discrete time delays that provide for biological factors and memory effects in the spread of disease. Caputo derivatives and fixed-point theory are implemented, and we identify the existence and uniqueness of solutions, as well as the basic reproduction number for both endemic and disease-free equilibria. Local stability is analyzed through characteristic equations and linearization, while numerical simulations confirm theoretical results and illustrate the influence of fractional order, delays, and parameters. The findings show that fractional-delay models provide a more flexible and effective framework for studying disease dynamics and control.