Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-space fabric underlying anomalous diffusion   This study unveils the time-space transforms underlying anomalous diffusion
process. Based on this finding, we present the two hypotheses concerning the
effect of fractal time-space fabric on physical behaviors and accordingly
derive fractional quantum relationships between energy and frequency, momentum
and wavenumber which further give rise to fractional Schrodinger equation. As
an alternative modeling approach to the standard fractional derivatives, we
introduce the concept of the Hausdorff derivative underlying the Hausdorff
dimensions of metric spacetime. And in terms of the proposed hypotheses, the
Hausdorff derivative is used to derive a linear anomalous transport-diffusion
equation underlying anomalous diffusion process. Its Green's function solution
turns out to be a new type of stretched Gaussian distribution and is compared
with that from the Richardson's diffusion equation.

24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph