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Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem

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Abstract

This work presents an effective numerical approach to solving variable-order multi-dimensional fractional optimal control problems. Utilizing well-known formulas such as the variable-order Caputo derivative and variable-order Riemann–Liouville integral, we determine the variable-order operational matrices and product operational matrices for the fractional Chelyshkov wavelet. By using the operational matrices, the process of solving the variable-order multi-dimensional fractional optimal control problem is simplified to a system of algebraic equations. Finally, using the Lagrange multiplier technique, we obtain the approximate cost function based on determining the state and control functions. We establish the convergence analysis and error bounds for the proposed method. To check the veracity of the presented method, we solve some numerical examples.

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Acknowledgements

The “University Grants Commission (UGC)" fellowship scheme provided financial support with NTA Ref. No. 201610127052 is gratefully acknowledged by the first author.

Funding

The “University Grants Commission (UGC)" fellowship scheme provided financial support with NTA Ref. No. 201610127052 is gratefully acknowledged by the first author.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Akanksha Singh, Ankur Kanaujiya & Jugal Mohapatra

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  1. Akanksha Singh
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  2. Ankur Kanaujiya
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  3. Jugal Mohapatra
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Contributions

AS: Writing-Original draft, Conceptualization, Methodology, Investigation, AK and JM: Conceptualization, Supervision, Writing-review and editing.

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Correspondence to Jugal Mohapatra.

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Singh, A., Kanaujiya, A. & Mohapatra, J. Chelyshkov wavelet method for solving multidimensional variable order fractional optimal control problem. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02083-7

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  • DOI: https://doi.org/10.1007/s12190-024-02083-7

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