In this chapter, we investigate a fractional-order delay differential model reflecting the dynamics of hepatitis C virus (HCV) replication in the presence of interferon- \(\alpha \) treatment. We consider a fractional-order in the model to represent the intermediate cellular interactions and intracellular delay of the viral life cycle and incorporate a discrete time-delay to justify the short-run memory. The fractional-order is also considered with existing model parameters to unify the units of the differential equations. We analyze the steady states and dynamical behavior of the model. We deduce a threshold parameter \({\mathcal R}_0\) (average number of newly infected cells produced by a single infected cell) in terms of the treatment efficacy parameter \(0\le \varepsilon <1\) and other parameters. The numerical simulations confirm that the suggested model with fractional-order and time-delay can provide accurate description of nonlinear biological systems with memory. The analyses presented here will give the reader an insight into the dynamics of HCV infection.