AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER 0 < α < 1

被引：18
|
作者：
Xu, Wenjing [1 ]
Xu, Wei [1 ]
Lu, Kai [2 ]
机构：
[1] Northwestern Polytech Univ, Sch Sci, West Youyi Rd,ADD 127, Xian 710129, Peoples R China
[2] South China Univ Technol, Sch Math, Wushan Rd,ADD 381, Guangzhou 510640, Peoples R China
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2020年 / 23卷 / 03期
基金：
中国国家自然科学基金;
关键词：
averaging principle; fractional derivative; stochastic differential equations; DIFFUSION;
D O I：
10.1515/fca-2020-0046
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents an averaging principle for fractional stochastic differential equations in R-n with fractional order 0 < alpha < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.
引用
收藏
页码：908 / 919
页数：12
相关论文
共 50 条
  • [41] Controllability discussion for fractional stochastic Volterra-Fredholm integro-differential systems of order 1 &lt; r &lt; 2
    Dineshkumar, Chendrayan
    Vijayakumar, Velusamy
    Udhayakumar, Ramalingam
    Shukla, Anurag
    Nisar, Kottakkaran Sooppy
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2023, 24 (05) : 1947 - 1979
  • [42] Robust stability of fractional-order systems with mixed uncertainties: The 0 &lt; α &lt; 1 case
    Zhang, Qing-Hao
    Lu, Jun-Guo
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 126
  • [43] H∞ control for singular fractional-order interval systems: The 0 &lt; α &lt; 1 case
    Zhang, Qing-Hao
    Lu, Jun-Guo
    ISA TRANSACTIONS, 2021, 110 : 105 - 116
  • [44] Positive real lemmas for singular fractional-order systems: the 0 &lt; α &lt; 1 case
    Zhang, Qing-Hao
    Lu, Jun-Guo
    IET CONTROL THEORY AND APPLICATIONS, 2020, 14 (18): : 2805 - 2813
  • [45] Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 &lt; q &lt; 2
    Shukla, Anurag
    Panda, Sumati Kumari
    Vijayakumar, Velusamy
    Kumar, Kamalendra
    Thilagavathi, Kothandabani
    FRACTAL AND FRACTIONAL, 2024, 8 (09)
  • [46] Impulse invariance-based method for the computation of fractional integral of order 0 &lt; α &lt; 1
    Ferdi, Youcef
    COMPUTERS & ELECTRICAL ENGINEERING, 2009, 35 (05) : 722 - 729
  • [47] A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1 &lt; α &lt; 2 with impulses
    Afreen, A.
    Raheem, A.
    Khatoon, A.
    JOURNAL OF CONTROL AND DECISION, 2024,
  • [48] An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 &lt; γ &lt; 2
    Johnson, Murugesan
    Vijayakumar, Velusamy
    FRACTAL AND FRACTIONAL, 2023, 7 (04)
  • [49] New results concerning to approximate controllability of fractional integro-differential evolution equations of order 1 &lt; r &lt; 2
    Mohan Raja, M.
    Vijayakumar, V.
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2022, 38 (03) : 509 - 524
  • [50] An Averaging Principle for Stochastic Fractional Differential Equations Driven by fBm Involving Impulses
    Liu, Jiankang
    Wei, Wei
    Xu, Wei
    FRACTAL AND FRACTIONAL, 2022, 6 (05)
12345