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The optimal behavior of solutions to fractional impulsive stochastic integro-differential equations and its control problems

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Abstract

In this paper, we study a new class of fractional nonlinear impulsive stochastic integro-differential equations with infinite delay in separable Hilbert spaces. Firstly, by using the measure of noncompactness, stochastic analysis theory, solution operators and suitable fixed point theorems, we prove the existence of mild solutions for these systems. Secondly, the existence of optimal mild solutions is obtained. Thirdly, we establish the controllability of the controlled fractional impulsive stochastic functional integro-differential systems with not instantaneous impulses. Finally, an example is provided to show the application of our results.

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Acknowledgements

The authors would like to thank the editor and the reviewers for their constructive comments and suggestions. 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, 734000, Gansu, People’s Republic of China

    Zuomao Yan & Xingxue Yan

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  1. Zuomao Yan
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Yan, Z., Yan, X. The optimal behavior of solutions to fractional impulsive stochastic integro-differential equations and its control problems. J. Fixed Point Theory Appl. 21, 12 (2019). https://doi.org/10.1007/s11784-018-0649-8

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