Most unconventional gas reservoirs are naturally fractured in nature and exhibit dual porosity characteristics. Hydraulic fracturing often alters the reservoir parameters around the wellbore, thus, potentially creating a rubble zone (stimulated reservoir volume-SRV) with distinctly different characteristics when compared to the outer zone. This problem could ideally be approximated as an equivalent flow problem around a horizontal wellbore in a composite naturally fractured domain. The computational package developed in the current study could be used in generating forward solutions for prediction of production transients in hydraulically fractured double porosity reservoirs. Additionally, as a part of an inverse analysis procedure, using relevant dimensionless parameters, it will be possible to characterize the composite naturally fractured reservoirs. A solution to the elliptical flow problem that considers flow into a horizontal wellbore in a truly composite naturally fractured reservoir is attempted. Mathieu modified functions are used to solve the elliptical flow problem. Stehfest algorithm is used for inversion of the Laplace space solutions back to real time domain. This generated solution is validated with other existing solutions by collapsing it into its subsets given in the literature. Forward solutions are generated for various dimensionless parameters. A graphic user interface (GUI) is developed to generate production decline curves. The interface elliptical coordinate does have a significant effect on the dual porosity signature of production transients in the case of mobility ratios higher than 10. It is observed that the mobility ratio, diffusivity ratio, storativity ratio, interporosity flow coefficient ratios of the inner, and outer regions exhibit significant effects on the decline curves experienced by this class of reservoirs.