On a nonlinear stochastic fractional differential equation of fluid dynamics

被引：1

作者：

Jornet, Marc ^{[1
]}

Nieto, Juan J. ^{[2
]}

机构：

[1] Departament de Matemàtiques, Universitat de València, Burjassot,46100, Spain

[2] CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Santiago de Compostela,15782, Spain

来源：

Physica D: Nonlinear Phenomena | 2024年 / 470卷

关键词：

Liouville equation - Nonlinear equations - Stochastic models;

D O I：

10.1016/j.physd.2024.134400

中图分类号：

学科分类号：

摘要：

We deal with a nonlinear stochastic fractional differential equation, in the Caputo and Itô senses, that generalizes important models of fluid dynamics, such as the Bagley–Torvik and the Basset equations. We investigate the integral formulation, existence, uniqueness, moment bounds, and continuity with respect to input data. Some conjectures are raised. © 2024 The Authors

引用

共 50 条

[1] Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
Liu, Junfeng
Yan, Litan
JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (01) : 307 - 347
[2] Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
Junfeng Liu
Litan Yan
Journal of Theoretical Probability, 2016, 29 : 307 - 347
[3] Solution of Nonlinear Fractional Stochastic Integro-Differential Equation
Ahmed, Hamdy M.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2016, 37 (02) : 105 - 113
[4] A stochastic differential equation analysis of cerebrospinal fluid dynamics
Raman K.
Fluids and Barriers of the CNS, 8 (1)
[5] On a nonlinear stochastic pseudo-differential equation driven by fractional noise
Liu, Junfeng
Yan, Litan
STOCHASTICS AND DYNAMICS, 2018, 18 (01)
[6] Analysis of a nonlinear variable-order fractional stochastic differential equation
Zheng, Xiangcheng
Zhang, Zhongqiang
Wang, Hong
APPLIED MATHEMATICS LETTERS, 2020, 107 (107)
[7] On a stochastic fractional partial differential equation with a fractional noise
Shi, Kehua
Wang, Yongjin
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2012, 84 (01) : 21 - 36
[8] Well-posedness and dynamics of a fractional stochastic integro-differential equation
Liu, Linfang
Caraballo, Tomas
PHYSICA D-NONLINEAR PHENOMENA, 2017, 355 : 45 - 57
[9] Dynamics of Fractional Stochastic Ginzburg-Landau Equation Driven by Nonlinear Noise
Lu, Hong
Wang, Linlin
Zhang, Mingji
MATHEMATICS, 2022, 10 (23)
[10] SOLVABILITY FOR A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
Guo, Yingxin
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 80 (01) : 125 - 138

← 1 2 3 4 5 →