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2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05
Fractional diffusion equations are abstract partial differential equations
that involve fractional derivatives in space and time. They are useful to
model anomalous diffusion, where a plume of particles spreads in a different
manner than the classical diffusion equation predicts. An initial value problem
involving a space-fractional diffusion equation is an abstract Cauchy
problem, whose analytic solution...
In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects...
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