Progress in Fractional Differentiation & Applications
Article Title
Abstract
In this work, we presented the numerical investigation on the dynamics of fractional Langevin equation which is driven by a fractional Brownian motion and Caputo-Fabrizio fractional derivative operator were utilized. The order of fractional derivative was considered to be ν = 2 − 2H , where H ∈ (1/2, 1) is the Hurst’s index. In the context of numerical schemes, we present different numerical approaches such as the discrete sequence of finite difference, to simplify the second-order ordinary derivative, while for the fractional derivative term, we presented the discrete approximation using simple quadrature formula. Additionally, for overdamped case (without inertial term), we used the Adams-Bashforth method corresponding to the Caputo-Fabrizio fractional derivative. The convergence and stability analysis of the obtained numerical solution were established in this study.
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/pfda/060402
Recommended Citation
Azis Rangaig, Norodin and Magompara Conding, Rowaidah
(2020)
"Numerics of Fractional Langevin Equation Driven by Fractional Brownian Motion Using Non-Singular Fractional Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 6:
Iss.
4, Article 2.
DOI: http://dx.doi.org/10.18576/pfda/060402
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol6/iss4/2