On the basis of a well-based model (Model I) developed in a previous work (Liu and Valko in SPE J 2019. ), in which a fractional production decline model is developed based on anomalous diffusion to structurally account for the heterogeneity related to the complex fracture network, we incorporate two more components, i.e., the tempered anomalous diffusion and a source term, in the present work to develop a generalized model, namely Model II. Because of the two new components, Model II is capable of physically considering both the scale lower bound of heterogeneity and the influx from the matrix into the conductive fracture system. It consequently enables the new model to describe the complete sequence of regimes for the production of the slightly compressible single-phase fluid from the fractured unconventional reservoirs. Then, in the case studies, the synthetic data used in the previous work are better fitted to the new type curves in all observed periods, which demonstrates the advantage of Model II over Model I regarding the late-time flow regimes. In addition, the good fit of other sets of synthetic data to the Model II type curves exhibits the claimed capabilities of the new model and indicates the production of this type could be well characterized by seven parameters, i.e., alpha, c, lambda(D), omega, sigma, tau, and EUR. Finally, the characteristics of Model II are further investigated by analyzing the effects of several parameters on the production performance, based on which some insights about the practice of developing unconventional reservoirs using massive hydraulic fracturing are provided.