Anthroponotic cutaneous leishmaniasis (ACL) is a neglected tropical disease transmitted by sandflies, with human hosts serving as the primary reservoir. The persistence of asymptomatic infections, emerging insecticide resistance, and limited public awareness complicate control efforts. In this study, we propose a novel fractional-order optimal control model that captures the biological and behavioral complexities of ACL transmission. The model incorporates asymptomatic carriers, insecticide-resistant vectors, and a dynamic awareness function governed by public health campaigns and behavioral memory. Four independent control strategies—treatment, insecticide spraying, bed net use, and awareness efforts—are optimized under a shared budget constraint. The use of Caputo fractional derivatives enables the modeling of memory-dependent processes such as delayed intervention effects and behavioral inertia. Necessary conditions for optimality are derived via a generalized Pontryagin's maximum principle, and numerical simulations are conducted to explore cost-effective intervention combinations. Results demonstrate that memory effects significantly enhance the long-term efficacy of awareness and treatment efforts and that optimal resource allocation strategies differ markedly from those predicted by classical integer-order models. This work provides a comprehensive and flexible framework for guiding sustainable ACL control policies in endemic settings.