A new approach for production data analysis in unconventional reservoirs is presented. Unlike the existing decline-curve analysis methods, this approach is not empirical and it is theoretically rigorous. The basis of the approach is an anomalous diffusion model for the performance of fractured horizontal wells surrounded by a stimulated reservoir volume. In the anomalous diffusion model, instead of Darcy's Law, a more general constitutional relation is used to incorporate the non-local and hereditary nature of flow in highly heterogeneous nanoporous media. The sub- or super-diffusive state of flow can be deduced from the slope of the straight line on the log-log plot of rate vs. time. Nonnecessity of a detailed description of the intrinsic properties and spatial distribution of matrix and fracture constitutes the practical advantage of the model. The reduced number of parameters can be conveniently estimated from production data and used in the anomalous diffusion model to predict future production. In this paper, a one-dimensional numerical model is implemented and applied to two Barnett shale gas wells and compared to common empirical models. It is shown that, even with limited completion, reservoir, and production data, the anomalous diffusion model has the potential to capture the production characteristics. Moreover, the model can be used to run sensitivities on actual system variables such as hydraulic fracture length, height and spacing, as well as to account for changing operating conditions.