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Approximate controllability of fractional neutral stochastic system with infinite delay. (English) Zbl 1263.93039
Summary: The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii’s fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
MSC:
93B05Controllability
34K37Functional-differential equations with fractional derivatives
34K50Stochastic functional-differential equations
60G22Fractional processes, including fractional Brownian motion
60H15Stochastic partial differential equations