Solvability and optimal controls of a fractional impulsive stochastic partial integro-differential equation with state-dependent delay. (English) Zbl 1395.45023
Summary: In this paper, a new class of fractional impulsive stochastic partial integro-differential control systems with state-dependent delay and their optimal controls in a Hilbert space is studied. We firstly prove an existence result of mild solutions for the control systems by using stochastic analysis, analytic \(\alpha\)-resolvent operator, fractional powers of closed operators and suitable fixed point theorems. Then we derive the existence conditions of optimal pairs to the fractional impulsive stochastic control systems. Finally, an example is given to illustrate the effectiveness of our main results.
MSC:
| 45K05 | Integro-partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 93E20 | Optimal stochastic control |
Keywords:
optimal controls; state-dependent delay; analytic \(\alpha\)-resolvent operator; fixed point theoremReferences:
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