Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay

作者：Yan, Zuomao^*; Lu, Fangxia

来源：Applied Mathematics and Computation, 2017, 292: 425-447.

DOI：10.1016/j.amc.2016.06.035

• Approximate controllability
• Multi-valued fractional impulsive stochastic partial integro-differential equations
• Infinite delay
• Analytic alpha-resolvent operator
• Fixed point theorem

In this paper, the approximate controllability of a new class of multi-valued fractional impulsive stochastic partial integro-differential equations with infinite delay in Hilbert spaces is studied. Firstly, by using stochastic analysis, analytic alpha-resolvent operator, fractional powers of closed operators and a fixed point theorem for multi-valued maps, we prove an existence result of mild solutions for the control systems under the mixed Lipschitz and Caratheodory conditions. Secondly, we discuss a new set of sufficient conditions for the approximate controllability of the systems. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the proposed theory.

• 出版日期2017-1-1
• 单位河西学院; 兰州大学