Next Article in Journal
Some New Fractional Trapezium-Type Inequalities for Preinvex Functions
Previous Article in Journal
On Analytic Functions Involving the q-Ruscheweyeh Derivative
Open AccessArticle

On the Fractal Langevin Equation

Young Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia, Iran
Fractal Fract 2019, 3(1), 11; https://doi.org/10.3390/fractalfract3010011
Received: 22 February 2019 / Revised: 7 March 2019 / Accepted: 12 March 2019 / Published: 13 March 2019
In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle- τ Cantor set. The fractal mean square displacement of different random walks on the middle- τ Cantor set are presented. Fractal under-damped and over-damped Langevin equations, fractal scaled Brownian motion, and ultra-slow fractal scaled Brownian motion are suggested and the corresponding fractal mean square displacements are obtained. The results are plotted to show the details. View Full-Text
Keywords: local fractal calculus; fractal mean square displacement; middle-τ Cantor sets; fractal Langevin equations local fractal calculus; fractal mean square displacement; middle-τ Cantor sets; fractal Langevin equations
Show Figures

Figure 1

MDPI and ACS Style

Khalili Golmankhaneh, A. On the Fractal Langevin Equation. Fractal Fract 2019, 3, 11.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop