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

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

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
170 KB
Volume
326
Category
Article
ISSN
0378-4371

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✦ Synopsis

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 proved that the asymptotic shape of its solution 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. Furthermore, it is shown that the solution of FFPE with parameter has the same properties as that ones of HFFPE.

📜 SIMILAR VOLUMES

Stretched Gaussian asymptotic behavior f
Stretched Gaussian asymptotic behavior for fractional Fokker–Planck equation on fractal structure in external force fields
✍ Yun Xu; Fu-Yao Ren; Jin-Rong Liang; Wei-Yuan Qiu 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 266 KB

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.