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Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets

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Abstract

This paper studies a numerical approach based on generalized fractional-order Chebyshev wavelets for solving distributed-order fractional optimal control problems (DO-FOCPs). The exact value of the Riemann–Liouville fractional integral operator of the given wavelets is computed by applying regularized beta function. The exact formula and collocation method are applied to transform the DO-FOCP to a new optimization problem. This new problem can be solved by the existing methods. Four examples are given to show the advantage of this method in comparison with the existing methods in the literature.

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Acknowledgements

The authors wish to express their sincere thanks to the anonymous referees for valuable suggestions that improved the final manuscript.

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  1. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS, 39762, USA

    Ghodsieh Ghanbari & Mohsen Razzaghi

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  1. Ghodsieh Ghanbari
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  2. Mohsen Razzaghi
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Correspondence to Mohsen Razzaghi.

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Ghanbari, G., Razzaghi, M. Numerical solutions for distributed-order fractional optimal control problems by using generalized fractional-order Chebyshev wavelets. Nonlinear Dyn 108, 265–277 (2022). https://doi.org/10.1007/s11071-021-07195-4

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  • DOI: https://doi.org/10.1007/s11071-021-07195-4

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