To improve the data rate in OFDMA-based wireless networks, Carrier Aggregation (CA) technology has been included in the LTE-Advanced standard. Different Carrier Component (CC) capacities of users under the same eNodeB (eNB, i.e. Base Station) make it challenging to allocate resources with CA. In this paper, we jointly consider CC and Resource Block (RB) assignments, and power allocation to achieve proportional fairness in the long term. The goal of the problem is to maximize the overall throughput with fairness consideration. We consider a more general CC assignment framework that each User Equipment (UE) (i.e. Mobile Station) can support any number of CCs. Furthermore, we have proved the problem is NP-hard, even if power is equally allocated to RBs. Thus, first an optimal RB assignment and power allocation algorithm is proposed and then a carrier aggregation enabled joint resource allocation algorithm called CARA is proposed. By jointly considering CC and RB assignments, and power allocation, the proposed approach can achieve better performance. Simulation results show the proposed algorithm can significantly improve performance, e.g., total throughput compared with the existing algorithm.