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Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

Long Shi ()

Advances in Mathematical Physics, 2019, vol. 2019, 1-5

Abstract: In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function . In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form . The anomy exponent varies from to when and from to when . The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.

Date: 2019
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DOI: 10.1155/2019/3479715

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