In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer [6]. More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential equations driven by Lévy processes. Basing on this representation, a self-contained proof for the existence of local unique solution for the fractal Navier-Stokes equation with initial data in W 1,p is provided, and in the case of two dimensions or large viscosity, the existence of global solution is also obtained. In order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for Lévy processes with time dependent and discontinuous drifts is proved.As for generalized Navier-Stokes equation (1.1), when L = −(−∆) α/2 , it has been studied by Wu [25] in Besov spaces by using purely analytic argument. The main feature of such fractal equations is that operator L given by (1.2) is non-local. Recently, there are increasing interests for studying such fractal equations or fractional dissipative equations since they naturally appear in hydrodynamics, statistcal mechanics, physiology, certain combustion models, and so on (cf. [21, 19,24], etc.).