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Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs

Author

Listed:
  • Hossein Hassani

    (Anand International College of Engineering)

  • Zakieh Avazzadeh

    (University of South Africa)

  • Praveen Agarwal

    (Anand International College of Engineering)

  • Mohammad Javad Ebadi

    (Chabahar Maritime University)

  • Ali Bayati Eshkaftaki

    (Shahrekord University)

Abstract

In this paper, we introduce a general class of coupled nonlinear systems of variable-order fractional partial differential equations (GCNSV-FPDEs) with initial and boundary conditions. We propose a hybrid method based on new generalized Bernoulli–Laguerre polynomials (GB-LPs) for solving GCNSV-FPDEs. The concept of variable-order fractional derivatives (V-FDs) is employed in the Caputo type. We extract the operational matrices (OMs) of classical and V-FDs of GB-LPs. By utilizing GB-LPs, OMs, and the Lagrange multipliers method, we transform the given GCNSV-FPDE into a system of algebraic equations to be solved. The proposed method yields satisfactory results even with a small number of GB-LPs. We provide a full verification of the method’s convergence, and two examples are included to demonstrate its validity and applicability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02346-6
    DOI: 10.1007/s10957-023-02346-6
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    References listed on IDEAS

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    1. Fakhrodin Mohammadi & Hossein Hassani, 2019. "Numerical Solution of Two-Dimensional Variable-Order Fractional Optimal Control Problem by Generalized Polynomial Basis," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 536-555, February.
    2. Zeghdane, Rebiha, 2019. "Numerical solution of stochastic integral equations by using Bernoulli operational matrix," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 238-254.
    3. Chi, Xiaoqing & Jiang, Xiaoyun, 2021. "Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    4. 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.
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