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A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems

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Abstract

We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann–Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz’s method. Examples show that the proposed approach is more accurate than recent methods available in the literature.

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Acknowledgments

This work is part of first author’s PhD project. It was partially supported by Islamic Azad University, Tehran, Iran, and CIDMA-FCT, Portugal, within project UID/MAT/04106/2013. Jahanshahi was also supported by a scholarship from the Ministry of Science, Research and Technology of the Islamic Republic of Iran, to visit the University of Aveiro, Portugal, and work with Professor Torres. The hospitality and the excellent working conditions at the University of Aveiro are here gratefully acknowledged. The authors are indebted to an anonymous referee for a careful reading of the original manuscript and for providing several suggestions, questions, and remarks. They are also grateful to the Editor-in-Chief, Professor Giannessi, and Ryan Loxton, for English improvements.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Salman Jahanshahi

  2. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

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  1. Salman Jahanshahi
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  2. Delfim F. M. Torres
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Correspondence to Delfim F. M. Torres.

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Jahanshahi, S., Torres, D.F.M. A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems. J Optim Theory Appl 174, 156–175 (2017). https://doi.org/10.1007/s10957-016-0884-3

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  • DOI: https://doi.org/10.1007/s10957-016-0884-3

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