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Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption

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Abstract

In this paper, an evolution system with a Riemann–Liouville fractional derivative is proposed and analyzed. With the help of a resolvent technique, a suitable concept of solutions to this system is formulated and the corresponding existence of solutions is demonstrated. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. Our work essentially generalizes previous results on optimal controls of all evolution systems. Finally, a simple example is presented to illustrate our theoretical results.

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Acknowledgements

The authors are grateful to the editor and the referees for their constructive comments and suggestions for the improvement in the paper. Furthermore, the work was supported by the NSF of China (11571300, 11271316), the Qing Lan Project of Jiangsu Province of China, the Graduate Research, Innovation Projects in Jiangsu Province (KYLX16-1382) and the High-Level Personnel Support Program of Yangzhou University.

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, People’s Republic of China

    Shouguo Zhu, Zhenbin Fan & Gang Li

  2. School of Mathematics, Taizhou College of Nanjing Normal University, Taizhou, 225300, People’s Republic of China

    Shouguo Zhu

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  1. Shouguo Zhu
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  2. Zhenbin Fan
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  3. Gang Li
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Correspondence to Zhenbin Fan.

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Zhu, S., Fan, Z. & Li, G. Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption. J Optim Theory Appl 174, 47–64 (2017). https://doi.org/10.1007/s10957-017-1119-y

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  • DOI: https://doi.org/10.1007/s10957-017-1119-y

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