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In this article, the continuous time random walk on the circle is studied. Wederive the corresponding generalized master equation and discuss the effects oftopology, especially important when Levy flights are allowed. Then, we work outthe fluid limit equation, formulated in terms of the periodic version of thefractional Riemann-Liouville operators, for which we provide explicitexpressions. Finally, we compute the propagator in some simple cases. Theanalysis presented herein should be relevant when investigating anomaloustransport phenomena in systems with periodic dimensions.

Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle