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Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces

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Abstract

This paper concerns the fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces. A suitable mild solution of the fractional finite time delay evolution systems is introduced. Using the singular version of the Gronwall inequality with finite time delay, we obtain some sufficient conditions for the existence, uniqueness and continuous dependence of mild solutions of these control systems. A formulation for the fractional Lagrange problem is introduced. The existence of optimal pairs of fractional-time-delay evolution systems is also presented. Finally, an example is given for demonstration.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China

    Jinrong Wang & Wei Wei

  2. Department of Mathematics, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China

    Yong Zhou

Authors
  1. Jinrong Wang
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  2. Wei Wei
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  3. Yong Zhou
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Corresponding author

Correspondence to Jinrong Wang.

Additional information

The first author acknowledges the support by the Tianyuan Special Funds of the National Natural Science Foundation of China (11026102) and Key Projects of Science and Technology Research in the Ministry of Education (211169). The third author acknowledges the support by National Natural Science Foundation of China (10971173).

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Wang, J., Wei, W. & Zhou, Y. Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces. J Dyn Control Syst 17, 515–535 (2011). https://doi.org/10.1007/s10883-011-9128-x

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  • DOI: https://doi.org/10.1007/s10883-011-9128-x

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