Fractional Green's function for fractional partial differential equations

Fractional order partial differential equations, as generalization of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we derive an explicit representation of the fractional Green's function for a class of fractional partial differential equations, then we present their solutions by integrals in terms of fractional Green's function. The solution of the fractional advection-dispersion equation is given as special case. The new approach introduces a promising tool for solving fractional partial differential equations.