Asymptotic behavior of stochastic lattice systems with a Caputo fractional time derivative

作者：Wang Yejuan; Xu Jiaohui; Kloeden Peter E^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2016, 135: 205-222.

DOI：10.1016/j_na_2016_01.020

• Mean-square global attracting set
• Lattice dynamical system
• Fractional stochastic differential equation
• Caputo fractional substantial time derivative

The asymptotic behavior of a stochastic lattice system with a Caputo fractional time derivative is investigated. In particular, the existence of a global forward attracting set in the weak mean-square topology is established. A general theorem on the existence of solutions for a fractional SDE in a Hilbert space under the assumption that the nonlinear term is weakly continuous in a given sense is established and applied to the lattice system. The existence and uniqueness of solutions for a more general fractional SDEs is also obtained under a Lipschitz condition.

• 出版日期2016-4
• 单位兰州大学