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Title
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An effective computational solver for fractal-fractional 2D integro-differential equations
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Type
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JournalPaper
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Keywords
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Fractal-fractional integro-differential equations; Mittag-Leffler kernel; Operational matrix; Chelyshkov polynomials; Convergence analysis.
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Abstract
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In this paper, we develop a computational approach for fractal-fractional integro-di erential 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 oper- ational 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 parame- ters. An error analysis is presented to demonstrate the convergence order of the approach. We demonstrate the e ectiveness and reliability of the proposed technique by solving numerical examples.
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Researchers
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Salameh Sedaghat (Second Researcher), Yadollah Ordokhani (Third Researcher), Parisa Rahimkhani (First Researcher)
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