From the space–time fractional integral of the continuous time random walk to the space–time fractional diffusion equations, a short proof and simulation

E.A. Abdel-Rehim

Physica A: Statistical Mechanics and its Applications, 2019, vol. 531, issue C

Abstract: In this paper, I prove the relation between the integral equation of the continuous time random walk (CTRW) and the space–time fractional diffusion equations by using the definitions of the Weyl fractional derivatives and integrals. I generalize a transformation theorem between the independent variables of the solution of the space–time fractional diffusion equation (stfde) and the solution of the space–time fractional Fokker–Planck equation(stffpe). I simulate the symmetric and the non symmetric random walks for the two mentioned models. I use the asymptotic behavior of the Mittag-Leffler function for generating the waiting time random variable and use the Lévy flight distribution function to generate the jump width random variable for the both models. The simulation results are investigated for different values of the space and time fractional orders.

Keywords: Continuous time random walk; Integral equation; Stochastic processes; Space–time fractional derivatives; Diffusion processes; Fokker–Planck equation; Simulation by Monte Carlo method; Mittag-Leffler function (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119309124
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119309124

DOI: 10.1016/j.physa.2019.121547

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().