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Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay

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Abstract

This paper considers fractional optimal control of a semilinear system with fixed delay in a reflexive Banach space. The existence and uniqueness of mild solution are obtained using the Weissinger’s fixed point theorem. The existence of optimal control for the system governed by fractional-order semilinear equation with fixed delay in state is presented. To show the effectiveness of the developed theory, an example is given.

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Acknowledgments

The author is grateful to the reviewers for their careful reading of the manuscript and valuable comments which improved the manuscript. I also thank the editors for their suggestions. Finally, I acknowledge the support by R&D Doctoral Research scheme for University faculty.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Surendra Kumar

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  1. Surendra Kumar
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Correspondence to Surendra Kumar.

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Communicated by Boris Vexler.

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Kumar, S. Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay. J Optim Theory Appl 174, 108–121 (2017). https://doi.org/10.1007/s10957-015-0828-3

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  • DOI: https://doi.org/10.1007/s10957-015-0828-3

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