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Fractional diffusion, waiting-time distributions, and Cattaneo-type equations
1998
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We discuss a generalized diffusion equation resulting from an additive two-state process, in combination with an asymptotically fractal ͑asymptotic power-law͒ waiting-time distribution. The obtained equation is an extension to previously discussed fractional diffusion equations. Our description leads to a mean squared displacement which describes enhanced, subballistic transport for long times. The short time behavior, however, is of a ballistic nature. This separation into two domains results
doi:10.1103/physreve.57.6409
fatcat:6t6b2jsnnjbx5nmhj5ms6jeeou