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A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel

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Abstract

The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Grönwall’s inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.

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Acknowledgements

The authors would like to express their sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.

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Authors and Affiliations

  1. Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

  3. University of Bojnord, Bojnord, Iran

    Amin Jajarmi

  4. Sahand University of Technology, Tabriz, Iran

    Mojtaba Hajipour

Authors
  1. Dumitru Baleanu
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  2. Amin Jajarmi
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  3. Mojtaba Hajipour
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Correspondence to Amin Jajarmi.

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Baleanu, D., Jajarmi, A. & Hajipour, M. A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel. J Optim Theory Appl 175, 718–737 (2017). https://doi.org/10.1007/s10957-017-1186-0

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  • DOI: https://doi.org/10.1007/s10957-017-1186-0

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