A new result on averaging principle for Caputo-type fractional delay stochastic differential equations with Brownian motion

被引：12
作者：
Zou, Jing [1 ]
Luo, Danfeng [1 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang, Guizhou, Peoples R China
来源：
APPLICABLE ANALYSIS | 2024年 / 103卷 / 08期
关键词：
Fractional stochastic differential equations; delay; existence; uniqueness; averaging principle; INTEGRODIFFERENTIAL EQUATIONS; STABILITY; EXISTENCE;
D O I：
10.1080/00036811.2023.2245845
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we mainly explore the averaging principle of Caputo-type fractional delay stochastic differential equations with Brownian motion. Firstly, the solutions of this considered system are derived with the aid of the Picard iteration technique along with the Laplace transformation and its inverse. Secondly, we obtain the unique result by using the contradiction method. In addition, the averaging principle is discussed by means of the Burkholder-Davis-Gundy inequality, Jensen inequality, Holder inequality and Gronwall-Bellman inequality under some hypotheses. Finally, an example with numerical simulations is carried out to prove the relevant theories.
引用
收藏
页码：1397 / 1417
页数：21
相关论文
共 47 条
[21]  
Khas'minskii R. Z., 1968, Kybernetika, V4, P260
[22]   Laplace transform and fractional differential equations [J].
Li Kexue ;
Peng Jigen .
APPLIED MATHEMATICS LETTERS, 2011, 24 (12) :2019-2023
[23]   Existence and uniqueness for solutions of mixed stochastic delay differential equations [J].
Liu, Weiguo ;
Yu, Qianyi ;
Zhang, Xinwen .
RESEARCH IN THE MATHEMATICAL SCIENCES, 2021, 8 (03)
[24]   Ulam-Hyers stability of Caputo-type fractional fuzzy stochastic differential equations with delay [J].
Luo, Danfeng ;
Wang, Xue ;
Caraballo, Tomas ;
Zhu, Quanxin .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 121
[25]   Some results on finite-time stability of stochastic fractional-order delay differential equations [J].
Luo, Danfeng ;
Tian, Mengquan ;
Zhu, Quanxin .
CHAOS SOLITONS & FRACTALS, 2022, 158
[26]   A novel result on averaging principle of stochastic Hilfer-type fractional system involving non-Lipschitz coefficients [J].
Luo, Danfeng ;
Zhu, Quanxin ;
Luo, Zhiguo .
APPLIED MATHEMATICS LETTERS, 2021, 122
[27]   EXISTENCE AND HYERS-ULAM STABILITY RESULTS FOR A CLASS OF FRACTIONAL ORDER DELAY DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES [J].
Luo, Danfeng ;
Luo, Zhiguo .
MATHEMATICA SLOVACA, 2020, 70 (05) :1231-1248
[28]   An averaging principle for stochastic fractional differential equations with time-delays [J].
Luo, Danfeng ;
Zhu, Quanxin ;
Luo, Zhiguo .
APPLIED MATHEMATICS LETTERS, 2020, 105
[29]   Sufficient conditions for existence and uniqueness of fractional stochastic delay differential equations [J].
Moghaddam, B. P. ;
Zhang, Lei ;
Lopes, A. M. ;
Tenreiro Machado, J. A. ;
Mostaghim, Z. S. .
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2020, 92 (03) :379-396
[30]   Existence and Stability Results for Caputo Fractional Stochastic Differential Equations with Levy Noise [J].
Umamaheswari, P. ;
Balachandran, K. ;
Annapoorani, N. .
FILOMAT, 2020, 34 (05) :1739-1751
12345