This work proposes a novel and comprehensive fractional-order model for the transmission dynamics and optimal control of a zoonotic avian–human influenza system involving two viral strains. The model distinguishes itself from classical approaches in three key aspects: (i) the use of Caputo fractional derivatives to incorporate memory effects and long-term temporal correlations in biological processes; (ii) the inclusion of three epidemiologically distinct compartments— humans, poultry, and a contaminated environment—each contributing to disease propagation; and (iii) the integration of nonlinear behavioral (awareness-driven) responses that modify transmission rates based on perceived infection risk. Six time-dependent control measures are embedded: vaccination, treatment for both human strains, culling of infected birds, environmental decontamination, and public awareness campaigns. An optimal control framework is formulated via a cost functional that jointly minimizes the health and economic burdens.