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- W2085754829 abstract "In this paper, the anomalous diffusion processes are modeled with partial differential equations of the fractional order that are then discussed in details. The anomalous diffusion can be characterized by the property that it no longer follows the Gaussian statistics and in particular one observes a deviation from the linear time dependence of the mean squared displacement. This is the case for many different phenomena including, e.g., the translocation dynamics of a polymer chain through a nanopore, charge carrier transport in amorphous semiconductors, laser cooling in quantum optical systems to mention only few of them. In this paper, we consider the case of the anomalous diffusion that shows a power‐low growth of the mean squared displacement in time.Our starting point is a stochastic formulation of the model in terms of the random walk processes. Following this line, a continuous time random walk model in form of a system of the integral equations of convolution type for the corresponding probability ..." @default.
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- W2085754829 date "2010-01-01" @default.
- W2085754829 modified "2023-09-26" @default.
- W2085754829 title "Fractional Calculus Models for the Anomalous Diffusion Processes and Their Analysis" @default.
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- W2085754829 doi "https://doi.org/10.1063/1.3526664" @default.
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