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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. 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).
    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. 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.
    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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