This paper proposes a fluid antenna (FA)-enabled mobile edge computing (MEC) scheme to minimize total system delay by leveraging FA mobility to enhance channel conditions and improve computational offloading efficiency. The scheme jointly optimizes computation offloading, antenna positioning, and CPU frequency to reduce latency. An alternating iterative algorithm based on the interior point method and particle swarm optimization (IPPSO) is introduced to solve the optimization problem. Numerical results show that the proposed scheme outperforms traditional fixed antenna positions in terms of transmission rates and delay reduction. The IPPSO algorithm demonstrates robust convergence properties, validating the effectiveness of the method. The FA-enabled MEC network includes N single-antenna users and a FA-enabled base station (BS). The BS's FAs are mobile within a local domain, while user antennas remain stationary. The system model considers uplink transmission from users to the BS, with the received signal expressed as a function of the antenna positions and channel conditions. The channel model accounts for the field response and phase differences in signal propagation. The computation offloading model considers federated learning (FL) tasks, with users either training locally or offloading tasks to the MEC server. The total training latency for each user is calculated based on local and offloaded training times. The optimization problem aims to minimize the sum latency by jointly optimizing offloading ratios, CPU frequencies, and antenna positions. The problem is decomposed into sub-problems, with the first sub-problem being a convex optimization problem solved using traditional methods, and the second sub-problem addressed using PSO. The IPPSO-based algorithm is shown to converge quickly and effectively reduce total latency compared to baseline schemes. The results demonstrate the potential of FA technology to enhance MEC performance by improving channel conditions and reducing delays.This paper proposes a fluid antenna (FA)-enabled mobile edge computing (MEC) scheme to minimize total system delay by leveraging FA mobility to enhance channel conditions and improve computational offloading efficiency. The scheme jointly optimizes computation offloading, antenna positioning, and CPU frequency to reduce latency. An alternating iterative algorithm based on the interior point method and particle swarm optimization (IPPSO) is introduced to solve the optimization problem. Numerical results show that the proposed scheme outperforms traditional fixed antenna positions in terms of transmission rates and delay reduction. The IPPSO algorithm demonstrates robust convergence properties, validating the effectiveness of the method. The FA-enabled MEC network includes N single-antenna users and a FA-enabled base station (BS). The BS's FAs are mobile within a local domain, while user antennas remain stationary. The system model considers uplink transmission from users to the BS, with the received signal expressed as a function of the antenna positions and channel conditions. The channel model accounts for the field response and phase differences in signal propagation. The computation offloading model considers federated learning (FL) tasks, with users either training locally or offloading tasks to the MEC server. The total training latency for each user is calculated based on local and offloaded training times. The optimization problem aims to minimize the sum latency by jointly optimizing offloading ratios, CPU frequencies, and antenna positions. The problem is decomposed into sub-problems, with the first sub-problem being a convex optimization problem solved using traditional methods, and the second sub-problem addressed using PSO. The IPPSO-based algorithm is shown to converge quickly and effectively reduce total latency compared to baseline schemes. The results demonstrate the potential of FA technology to enhance MEC performance by improving channel conditions and reducing delays.