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Fairness with a α parameter is an important consideration to provide uniform and high quality service for each user when designing a wireless communication system. In general, α-fairness problem includes the proportional fairness and the max-min fairness. In this paper, we consider the problem of α-fairness-based joint power allocation and power splitting for massive multiple-input and multiple-output (MIMO) systems with simultaneous wireless information and power transfer (SWIPT). Different from the existing works, we utilize a low-complexity parametric optimization method to solve the non-convex proportional fairness problem. Furthermore, we develop a joint iterative algorithm to solve the general α-fairness problem and obtain the suboptimal solutions on power allocation and power splitting. Simulation results illustrate the performance of the proposed algorithm.