Abstract
We consider a new type of random walks of particles with a jump-like change in acceleration. The corresponding kinetic equations for the probability density of the particle coordinates are derived. The probability density is found to obey the fractional diffusion equation. In this case, both sub-and superdiffusion appear for a sufficiently rapidly decaying distribution of the random waiting times, which was not observed earlier and is a fundamentally new phenomenon in the theory of anomalous diffusion.
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