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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Computational Technique for Nonlinear Nonlocal Stochastic Dynamical Systems with Variable Order Fractional Brownian Noise

Journal of Applied Nonlinear Dynamics 12(1) (2023) 75--85 | DOI:10.5890/JAND.2023.03.005

A. Shahnazi-Pour$^1$, B. Parsa Moghaddam$^1$, A. Babaei$^2$

$^1$ Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

$^2$ Department of Mathematics, University of Mazandaran, Babolsar, Iran

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Abstract

This paper proposes a computationally technique for simulating solutions of nonlinear nonlocal stochastic dynamical systems driven by variable-order fractional Brownian motion with Hurst index. The value of the Hurst index depends on time $t$ belong to interval $(\frac{1}{2},1)$. The proposed technique is adopted quadratic interpolation for fractional-order derivative. Moreover, it is exploited in the discussion of fractional stochastic financial and pendulum dynamical systems. The proficiency of the presented technique is confirmed by using of investigating statistical indicators for the stochastic approximations for various values of fractional order parameters.

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