Unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) is regarded as a key enabler for next-generation wireless systems. However, conventional fixed-position antennas limit the ability of UAVs to fully exploit their inherent potential. To overcome this limitation, we propose a UAV-enabled ISAC framework equipped with fluid antennas (FAs), where the mobility of antenna elements introduces additional spatial degrees of freedom to simultaneously enhance communication and sensing performance. A multi-objective optimization problem is formulated to maximize the communication rates of multiple users while minimizing the Cramér-Rao bound (CRB) for the angle estimation of a single target. Due to excessively frequent updates of FA positions may lead to response delay, a three-timescale optimization framework is developed to jointly optimize transmit beamforming, FA positions, and UAV trajectory based on their characteristics. To solve the non-convexity of the problem, an alternating optimization-based algorithm is developed to obtain a sub-optimal solution. Numerical results show that the proposed scheme significantly outperforms various benchmark schemes, validating the effectiveness of integrating the FA technology into the UAV-enabled ISAC systems.

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