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An optimum method for fractal–fractional optimal control and variational problems

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Abstract

In this paper, we design a new computational algorithm for solving fractal–fractional optimal control and variational problems. To attain the proposed goal, we exert Pell–Lucas polynomials and the Legendre–Gauss quadrature rule. Also, to improve the accuracy of the numerical scheme, we present a new method for calculating the operational matrix of FF-derivative. The proposed operational matrix is called pseudo-operational matrix which is in comparison with the usual operational matrix is more accurate. Furthermore, the experimental results including a comparison to another method are expressed in the last section.

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Acknowledgements

We express our sincere thanks to the anonymous referees for their valuable suggestions that improved the final manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical sciences, Alzahra University, Tehran, Iran

    Haniye Dehestani & Yadollah Ordokhani

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  1. Haniye Dehestani
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Dehestani, H., Ordokhani, Y. An optimum method for fractal–fractional optimal control and variational problems. Int. J. Dynam. Control 11, 229–241 (2023). https://doi.org/10.1007/s40435-022-00978-6

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  • DOI: https://doi.org/10.1007/s40435-022-00978-6

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