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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, India

    Hossein Hassani & Praveen Agarwal

  2. Department of Mathematical Sciences, University of South Africa, Florida, South Africa

    Zakieh Avazzadeh

  3. Department of Mathematics, Chabahar Maritime University, Chabahar, Iran

    Mohammad Javad Ebadi

  4. Faculty of Mathematics, Shahrekord University, Shahrekord, Iran

    Ali Bayati Eshkaftaki

Authors
  1. Hossein Hassani
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  2. Zakieh Avazzadeh
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  3. Praveen Agarwal
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  4. Mohammad Javad Ebadi
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  5. Ali Bayati Eshkaftaki
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Correspondence to Hossein Hassani.

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Hassani, H., Avazzadeh, Z., Agarwal, P. et al. Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs. J Optim Theory Appl 200, 371–393 (2024). https://doi.org/10.1007/s10957-023-02346-6

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