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Federated learning (FL) offers many benefits, such as better privacy preservation and less communication overhead for scenarios with frequent data generation. In FL, local models are trained on end-devices and then migrated to the network edge or cloud for global aggregation. This aggregated model is shared back with end-devices to further improve their local models. This iterative process continues until convergence is achieved. Although FL has many merits, it has many challenges. The prominent one is computing resource constraints. End-devices typically have fewer computing resources and are unable to learn well the local models. Therefore, split FL (SFL) was introduced to address this problem. However, enabling SFL is also challenging due to wireless resource constraints and uncertainties. We formulate a joint end-devices computing resources optimization, task-offloading, and resource allocation problem for SFL at the network edge. Our problem formulation has a mixed-integer non-linear programming problem nature and hard to solve due to the presence of both binary and continuous variables. We propose a double deep Q-network (DDDQN) and optimization-based solution. Finally, we validate the proposed method using extensive simulation results.