  Einstein's theory of Brownian motion is revisited in order to formulate
generalized kinetic theory of anomalous diffusion. It is shown that if the
assumptions of analyticity and the existence of the second moment of the
displacement distribution are relaxed, the fractional derivative naturally
appears in the diffusion equation. This is the first demonstration of the
physical origin of the fractional derivative, in marked contrast to the usual
phenomenological introduction of it. Furthermore, Einstein's approach is
generalized to nonlinear kinetic theory to derive the porous-medium-type
equation by the appropriate use of the escort distribution.
