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Approximate Optimal Control of Fractional Impulsive Partial Stochastic Differential Inclusions Driven by Rosenblatt Process

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Abstract

In this paper, we study the approximate optimal control problems for a class of fractional partial stochastic differential inclusions driven by Rosenblatt process and non-instantaneous impulses in a Hilbert space. Firstly, we prove an existence result of mild solutions for the control systems by using stochastic analysis, the fractional calculus, the measure of noncompactness, properties of sectorial operators and fixed point theorems. Secondly, we derive the existence conditions of approximate solutions to optimal control problems governed by fractional impulsive partial stochastic differential control systems with the help of minimizing sequence method. Finally, an example is given for the illustration of the obtained theoretical results.

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Acknowledgements

This work is supported by the Natural Science Foundation of Gansu Provincial (23JRRG0006), Faculty Research Grants Awarded by Principal’s Funds(CXTD2023006).

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  1. Department of Mathematics, Hexi University, Zhangye, 734000, Gansu, People’s Republic of China

    Zuomao Yan

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Yan, Z. Approximate Optimal Control of Fractional Impulsive Partial Stochastic Differential Inclusions Driven by Rosenblatt Process. Appl Math Optim 89, 3 (2024). https://doi.org/10.1007/s00245-023-10071-9

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