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Solvability and Optimal Controls of a Fractional Impulsive Stochastic Partial Integro-Differential Equation with State-Dependent Delay

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Abstract

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.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11461019), the President Fund of Scientific Research Innovation and Application of Hexi University (xz2013-10).

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  1. Department of Mathematics, Hexi University, Zhangye, Gansu, 734000, P.R. China

    Zuomao Yan & Fangxia Lu

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  1. Zuomao Yan
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  2. Fangxia Lu
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Correspondence to Zuomao Yan.

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Yan, Z., Lu, F. Solvability and Optimal Controls of a Fractional Impulsive Stochastic Partial Integro-Differential Equation with State-Dependent Delay. Acta Appl Math 155, 57–84 (2018). https://doi.org/10.1007/s10440-017-0145-y

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