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A new Legendre operational technique for delay fractional optimal control problems

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Abstract

In this paper, new operational matrices for shifted Legendre orthonormal polynomial are derived. This polynomial is used as a basis function for developing a new numerical technique for the delay fractional optimal control problem. The fractional integral is described in the Riemann–Liouville sense, while the fractional derivative is described in the Caputo sense. The operational matrix of fractional integrals is used together with the Lagrange multiplier method for the constrained extremum in order to minimize the performance index. The problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Three numerical examples of different types of delay fractional optimal control problems are implemented with their approximate solutions for confirming the high accuracy and applicability of the proposed method.

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Acknowledgments

The authors are very grateful to the referees for carefully reading the paper and for their comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    A. H. Bhrawy

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    A. H. Bhrawy

  3. Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja, 72511, Egypt

    S. S. Ezz-Eldien

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Bhrawy, A.H., Ezz-Eldien, S.S. A new Legendre operational technique for delay fractional optimal control problems. Calcolo 53, 521–543 (2016). https://doi.org/10.1007/s10092-015-0160-1

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