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Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses

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Abstract

This paper is concerned on optimal control problems for systems governed semilinear fractional differential equations with not instantaneous impulses in the infinite dimensional spaces. We utilize fractional calculus, semigroup theory and fixed point approach to present the solvability of the corresponding control system by using the new introduced concept of mild solutions. Next, we give the existence result of optimal controls for Lagrange problem under the suitable conditions. Finally, an example is given to illustrate the effectiveness of our results.

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Acknowledgements

The authors thank the referees for their careful reading of the manuscript and insightful comments. This work is supported by National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Unite Foundation of Guizhou Province ([2015]7640), and Graduate ZDKC([2015]003).

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, People’s Republic of China

    Shengda Liu & JinRong Wang

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  1. Shengda Liu
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  2. JinRong Wang
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Correspondence to JinRong Wang.

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Liu, S., Wang, J. Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses. J Optim Theory Appl 174, 455–473 (2017). https://doi.org/10.1007/s10957-017-1122-3

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  • DOI: https://doi.org/10.1007/s10957-017-1122-3

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