Journal
EUROPHYSICS LETTERS
Volume 51, Issue 5, Pages 492-498Publisher
E D P SCIENCES
DOI: 10.1209/epl/i2000-00364-5
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Superdiffusion in the sub-ballistic regime with a non-diverging mean-squared displacement is studied on the basis of a linear, fractional kinetic equation with constant coefficients which is non-local in time and leads to an exponential tail of the corresponding probability density function. It is shown that sub-ballistic superdiffusion can be regarded as ballistic motion with a memory, much as slow diffusion can be thought of as a random walk with a memory. This suggests that fractional kinetic equations are useful in describing both sub- and superdiffusion processes.
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