# Generalized Space–Time Fractional Dynamics in Networks and Lattices

Abstract : We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the time-fractional Poisson renewal process. This process introduces a non-Markovian walk with long-time memory effects and fat-tailed characteristics in the waiting time density. We analyze generalized space-time fractional diffusion' in the infinite $\it d$-dimensional integer lattice $\it \mathbb{Z}^d$. We obtain in the diffusion limit a macroscopic' space-time fractional diffusion equation. Classical CTRW models such as with Laskin's fractional Poisson process and standard Poisson process which occur as special cases are also analyzed. The developed generalized space-time fractional CTRW model contains a four-dimensional parameter space and offers therefore a great flexibility to describe real-world situations in complex systems.
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https://hal.archives-ouvertes.fr/hal-02314815
Contributor : Thomas Michelitsch <>
Submitted on : Sunday, October 13, 2019 - 8:48:57 PM
Last modification on : Wednesday, December 9, 2020 - 3:12:06 PM
Long-term archiving on: : Tuesday, January 14, 2020 - 1:44:31 PM

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Thomas Michelitsch, Alejandro Perez Riascos, Bernard Collet, Andrzej F. Nowakowski, Franck Nicolleau. Generalized Space–Time Fractional Dynamics in Networks and Lattices. H Altenbach, V Eremeyev, I Pavlov, A. Porubov. Nonlinear Wave Dynamics of Materials and Structures. Advanced Structured Materials, 122, Springer, Cam, pp.221-249, 2020, Advanced Structured Materials, 978-3-030-38707-5. ⟨10.1007/978-3-030-38708-2_14⟩. ⟨hal-02314815⟩

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