Time-space fabric underlying anomalous diffusion

By W. Chen. 2005

457 citations recorded by the source corpus.

Abstract 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 turn out to be a stretched Gaussian distribution and is compared with that from the Richardson’s turbulence diffusion equation.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/68dcb029466d4d8f122085225e75d334ee11efbb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Peiyi Shen
2. Hari M. Srivastava
3. Wei Wei
4. Lei Wang
5. Jing Zhang
6. Yunyi Zhang
7. Dumitru Băleanu
8. Xiao-jun Yang

In Statistical and Nonlinear Physics

1. Peiyi Shen
2. Hari M. Srivastava
3. Wei Wei
4. Lei Wang
5. Jing Zhang
6. Yunyi Zhang

Citations in the corpus

• Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[128] W.”
• Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space (2011, unknown): “Local fractional derivative had been introduced in [12–36]; that is the local fractional derivative was structured in [12–18, 26, 30–36], Jumarie gave the modified Riemann-Liouville derivative in [19, 20], the fractal derivative was considered in [21–25, 27–29], and the generalized fractal derivativ”
• Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, unknown): “[39, 40], the fractal derivative of Parvate et al.”
• A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “Definition 8 Chen’s definition is as follows [63, 64]”
• A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality (2014, methodology): “Some of the concepts of the local fractional derivative were established in [3–26].”