2019/10/14 by Thomas M. Michelitsch, Michelitsch, Thomas M., Alejandro P. Riascos +7
Mathematics · #FOS: Physical sciences #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · doi:10.48550/arxiv.1910.05949
openalex publication_date 2019/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℤd. 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.