具有时滞的模糊分数阶随机微分方程的存在性
Existence in Fuzzy Fractional Stochastic Differential Equations with Time-Delays
DOI: 10.12677/ORF.2023.136620, PDF,  被引量    国家自然科学基金支持
作者: 唐浦森：贵州大学数学与统计学院，贵州 贵阳；陈 琳*：常熟理工学院数学与统计学院，江苏 常熟
关键词: 分数阶微积分；模糊；随机微分方程；存在性；Fractional Calculus； Fuzzy； Stochastic Differential Equations； Existence
摘要: 本文研究了一类具有时滞的Caputo型模糊分数阶随机微分方程。利用随机分析技术和Banach不动点定理，得到了所考虑系统解的存在唯一性。最后，我们提出一个例子来说明理论结果。
Abstract: In this article, we investigate a class of Caputo type fuzzy fractional order stochastic differential equations with time-delays. By using stochastic analysis techniques and Banach’s fixed point theorem, we obtain the existence and uniqueness for the solutions of the considered system. At last, we present an example to illustrate the theoretical results.
文章引用：唐浦森, 陈琳. 具有时滞的模糊分数阶随机微分方程的存在性[J]. 运筹与模糊学, 2023, 13(6): 6277-6288. https://doi.org/10.12677/ORF.2023.136620

参考文献

[1] Gibbs, J. (1960) Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics. Cambridge University Press, New York.
[2] Evans, L. (2013) An Introduction to Stochastic Differential Equations. American Mathematical Society, Providence. [Google Scholar] [CrossRef] 
[3] Gikhman, I. and Skorokhod, A. (2007) Stochastic Differential Equations. In: Gikhman, I. and Skorokhod, A., Eds., The Theory of Stochastic Processes III, Springer, Berlin, 113-219. [Google Scholar] [CrossRef] 
[4] Särkkä, S. (2019) Applied Stochastic Differential Equa-tions. Cambridge University, Cambridge. [Google Scholar] [CrossRef] 
[5] Øksendal, B. (2003) Stochastic Differential Equations. Springer, Berlin. [Google Scholar] [CrossRef] 
[6] Zadeh, L. (1965) Fuzzy Sets. Information and Control, 8, 338-353. [Google Scholar] [CrossRef] 
[7] Zadeh, L. (1978) Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1, 3-28. [Google Scholar] [CrossRef] 
[8] Zimmermann, H. (1992) Fuzzy Set Theory—And Its Applications. Springer, Boston. [Google Scholar] [CrossRef] 
[9] Jafari, H. and Malinowski, M. (2023) Symmetric Fuzzy Stochastic Differential Equations Driven by Fractional Brownian Motion. Symmetry, 15, Article 1436. [Google Scholar] [CrossRef] 
[10] Jafari, H., Malinowski, M. and Ebadi, M. (2021) Fuzzy Stochastic Differential Equations Driven by Fractional Brownian Motion. Advances in Difference Equations, 2021, Article No. 16. [Google Scholar] [CrossRef] 
[11] Malinowski, M. (2020) Symmetric Fuzzy Stochastic Differential Equations with Generalized Global Lipschitz Condition. Symmetry, 12, Article 819. [Google Scholar] [CrossRef] 
[12] Abuasbeh, K. and Shafqat, R. (2022) Fractional Brownian Motion for a System of Fuzzy Fractional Stochastic Differential Equation. Journal of Mathematics, 2022, Article ID: 3559035. [Google Scholar] [CrossRef] 
[13] Malinowski, M. (2012) Random Fuzzy Differential Equations under Generalized Lipschitz Condition. Nonlinear Analysis: Real World Applications, 13, 860-881. [Google Scholar] [CrossRef] 
[14] Malinowski, M. (2016) Stochastic Fuzzy Differential Equations of a Nonincreasing Type. Communications in Nonlinear Science and Numerical Simulation, 33, 99-117. [Google Scholar] [CrossRef] 
[15] Malinowski, M. and Michta, M. (2011) Stochastic Fuzzy Differential Equations with an Application. Kybernetika, 47, 123-143.
[16] Vu, H. (2017) Random Fuzzy Dif-ferential Equations with Impulses. Complexity, 2017, Article ID: 4056016. [Google Scholar] [CrossRef] 
[17] Ma, W. and Li, X. (2017) Itô Type Stochastic Fuzzy Differential Equations with Infinite Delay. Applied Mathematics, 30, 726-736.
[18] Malinowski, M. (2009) On Random Fuzzy Differential Equations. Fuzzy Sets and Systems, 160, 3152-3165. [Google Scholar] [CrossRef] 
[19] Malinowski, M. (2012) Itô Type Stochastic Fuzzy Differential Equations with Delay. Systems & Control Letters, 61, 692-701. [Google Scholar] [CrossRef] 
[20] Malinowski, M. (2012) Strong Solutions to Stochastic Fuzzy Differential Equationsof Itô Type. Mathematical and Computer Modelling, 55, 918-928. [Google Scholar] [CrossRef] 
[21] Malinowski, M. (2013) Some Properties of Strong Solutions to Stochastic Fuzzy Differential Equations. Information Sciences, 252, 62-80. [Google Scholar] [CrossRef] 
[22] Lupulescu, V., Dong, L. and Van, N. (2015) Existence and Uniqueness of Solutions for Random Fuzzy Fractional Integral and Differential Equations. Journal of Intelligent & Fuzzy Systems, 29, 27-42. [Google Scholar] [CrossRef] 
[23] Vu, H., An, V. and Hoa, V. (2019) Random Fractional Differential Equations With Riemann-Liouville-Type Fuzzy Differentiability Concept. Journal of Intelligent & Fuzzy Systems, 36, 6467-6480. [Google Scholar] [CrossRef] 
[24] Priyadharsini, J. and Balasubramaniam, P. (2020) Ex-istence of Fuzzy Fractional Stochastic Differential System with Impulses. Computational and Applied Mathematics, 39, Article No. 195. [Google Scholar] [CrossRef] 
[25] Priyadharsini, J. and Balasubramaniam, P. (2022) Solvability of Fuzzy Fractional Stochastic Pantograph Differential System. Iranian Journal of Fuzzy Systems, 19, 47-60.
[26] Mazandarani, M., Pariz, N. and Kamyad, A. (2017) Granular Differentiability of Fuzzy-Number-Valued Functions. IEEE Transactions on Fuzzy Systems, 26, 310-323. [Google Scholar] [CrossRef] 
[27] Luo, D., Wang, X., Caraballo, T. and Zhu, Q. (2023) Ulam-Hyers Stability of Caputo-Type Fractional Fuzzy Stochastic Differential Equations with Delay. Communica-tions in Nonlinear Science and Numerical Simulation, 121, Article ID: 107229. [Google Scholar] [CrossRef] 
[28] Long, H. (2018) On Random Fuzzy Fractional Partial In-tegro-Differential Equations under Caputo Generalized Hukuhara Differentiability. Computational and Applied Mathematics, 37, 2738-2765. [Google Scholar] [CrossRef] 
[29] Vu, H., Hoa, N., Son, N. and O’Regane, D. (2018) Results on Initial Value Problems for Random Fuzzy Fractional Functional Differential Equations. Filomat, 32, 2601-2624. [Google Scholar] [CrossRef] 
[30] Wang, X., Luo, D. and Zhu, Q. (2022) Ulam-Hyers Stability of Caputo Type Fuzzy Differential Equations with Time- Delays. Chaos, Solitons & Fractals, 156, Article ID: 111822. [Google Scholar] [CrossRef] 
[31] Ngo, H., Lupulescu, V. and O’Regan, D. (2018) A Note on Initial Value Problems for Fractional Fuzzy Differential Equations. Fuzzy Sets and Systems, 347, 54-69. [Google Scholar] [CrossRef] 
[32] Malinowski, M. (2015) Random Fuzzy Fractional Integral Equations—Theoretical Foundations. Fuzzy Sets and Systems, 265, 39-62. [Google Scholar] [CrossRef] 

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