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A generalized fuzzy barycentric Lagrange interpolation method for solving two-dimensional fuzzy fractional Volterra integral equations

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Abstract

In this paper, a generalized fuzzy barycentric Lagrange interpolation method is proposed to solve two-dimensional fuzzy fractional Volterra integral equations. Firstly, we use the generalized Gronwall inequality and iterative methods to demonstrate the existence and uniqueness of solutions to the original equation. Secondly, combining the generalized fuzzy interpolation method and the fuzzy Gauss-Jacobi quadrature formula to discretize the original equation into corresponding algebraic equations in fuzzy environment. Then, the convergence of the proposed method is analyzed, and an error estimate is given based on the uniform continuity modulus. Finally, some numerical experiments show that the proposed method has high numerical accuracy for both smooth and non-smooth solutions.

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Acknowledgements

The authors are very grateful to the reviewers for their detailed comments and valuable suggestions, which improved the paper.

Funding

This work was partially supported by the financial support from the National Natural Science Foundation of China (12101089).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Ting Deng, Jin Huang & Yifei Wang

  2. School of Mathematics, Chengdu Normal University, Chengdu, Sichuan, 611130, China

    Hu Li

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  1. Ting Deng
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  2. Jin Huang
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All authors wrote the main manuscript text including Section 1–Section 7. All authors reviewed the manuscript.

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Correspondence to Jin Huang.

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Deng, T., Huang, J., Wang, Y. et al. A generalized fuzzy barycentric Lagrange interpolation method for solving two-dimensional fuzzy fractional Volterra integral equations. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01814-y

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