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An effective computational solver for fractal-fractional 2D integro-differential equations

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Abstract

In this paper, we develop a computational approach for fractal-fractional integro-differential equations (FFIDEs) in Atangana–Riemann–Liouville sense. This plan focuses on the Chelyshkov polynomials (ChPs) and the utilization of the Legendre–Gauss quadrature rule. The operational matrices (OMs) of integration, integer-order derivative and fractal-fractional-order derivative are calculated. These matrices in comparison to OMs existing in other methods are more accurate. The method consists of approximating the exiting functions in terms of basis functions. Using the provided OMs alongside the Legendre collocation points, the original problem is converted into a set of nonlinear algebraic equations containing unknown parameters. An error analysis is presented to demonstrate the convergence order of the approach. We demonstrate the effectiveness and reliability of the proposed technique by solving numerical examples.

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Acknowledgements

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the paper.

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Authors and Affiliations

  1. Faculty of Science, Mahallat Institute of Higher Education, Mahallat, Iran

    P. Rahimkhani

  2. Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

    S. Sedaghat

  3. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Y. Ordokhani

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  1. P. Rahimkhani
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  2. S. Sedaghat
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  3. Y. Ordokhani
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Rahimkhani, P., Sedaghat, S. & Ordokhani, Y. An effective computational solver for fractal-fractional 2D integro-differential equations. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02099-z

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