This work proposes a novel boundary-element based approach to model fluid transport in unconventional shale gas reservoirs with complex hydraulic fracture networks. The fluid flow model employed in this work considers multiple fluid transport mechanisms identified in in gas transporting process in shale nanopores including diffusion, sorption Kinetics, Knudsen diffusion, and sorbed-phase surface diffusion. Accordingly, two governing partial differential equations (PDEs) are written for free and sorbed gases. In the proposed method, boundary integral formulations are analytically derived using the fundamental solution of the Laplace Equation for two governing nonlinear PDEs and Green's second identity. The domain integrals considering the nonlinear terms due to multi-mechanism effects, are transformed into boundary integrals employing the dual reciprocity method (DRM). The resulting boundary integral equations for free and sorbed gas later are solved in terms of a series of discrete nodes after coupling with fracture flow model. The validity of proposed solution is verified using several case studies through comparison with a commercial finite-element numerical simulator COMSOL.