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A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems

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  • Postavaru, Octavian
  • Toma, Antonela

Abstract

We present, an accurate and efficient computational method based on the fractional-order hybrid of block-pulse functions and Bernoulli polynomials for solving fractional optimal control problems. The Riemann–Liouville fractional integral operator for the fractional-order hybrid of block-pulse functions and Bernoulli polynomials is constructed. The original problem is transformed to a system of algebraic equations which can be solved easily. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method.

Suggested Citation

  • Postavaru, Octavian & Toma, Antonela, 2022. "A numerical approach based on fractional-order hybrid functions of block-pulse and Bernoulli polynomials for numerical solutions of fractional optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 269-284.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:269-284
    DOI: 10.1016/j.matcom.2021.12.001
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    References listed on IDEAS

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    1. N. Haddadi & Y. Ordokhani & M. Razzaghi, 2012. "Optimal Control of Delay Systems by Using a Hybrid Functions Approximation," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 338-356, May.
    2. Mohsen Razzaghi & Hamid-Reza Marzban, 2000. "Direct method for variational problems via hybrid of block-pulse and chebyshev functions," Mathematical Problems in Engineering, Hindawi, vol. 6, pages 1-13, January.
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    Cited by:

    1. Hossein Hassani & Zakieh Avazzadeh & Praveen Agarwal & Mohammad Javad Ebadi & Ali Bayati Eshkaftaki, 2024. "Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 371-393, January.
    2. Postavaru, Octavian, 2023. "An efficient numerical method based on Fibonacci polynomials to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 406-422.

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