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Stretched Gaussian asymptotic behavior for fractional Fokker–Planck equation on fractal structure in external force fields

✍ Scribed by Yun Xu; Fu-Yao Ren; Jin-Rong Liang; Wei-Yuan Qiu

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 266 KB
Volume: 20
Category: Article
ISSN: 0960-0779
DOI: 10.1016/s0960-0779(03)00416-8

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✦ Synopsis

In this paper, it is proven that the asymptotic shape of the solution of the fractional Fokker-Planck equation is a stretched Gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for generic potentials.

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Fractional Fokker–Planck equation on heterogeneous fractal structures in external force fields and its solutions

✍ Fu-Yao Ren; Jin-Rong Liang; Wei-Yuan Qiu; Yun Xu 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 170 KB

We introduce a heterogeneous fractional Fokker-Planck equation (HFFPE) involving external force ÿelds describing systems on heterogeneous fractal structure medium. The HFFPE is shown to obey generalized Einstein relation, and its stationary solution is the generalized Boltzmann distribution. It is p